Speed and Velocity MCQ Quiz - Objective Question with Answer for Speed and Velocity - Download Free PDF

The correct answer is metre per second (m/s).Key Points

• The basic unit of speed of an object is metre per second (m/s).
• The speed of an object is defined as the rate at which it covers a distance in a given time.
• It is used to express the speed of objects that move relatively faster than the speed of light.

Additional Information

• Metre per km (m/km) is not a standard unit of speed.
• Metre per hour (m/h) is a unit of speed but it is not the basic unit of speed.
  • It is used to express the speed of objects that move relatively slower than the speed of light.
• Metre per minute (m/m) is also not the basic unit of speed.
  • It is used to express the speed of objects that move relatively slower than the speed of light.

CONCEPT:

Centripetal Acceleration (a_c): 

• Acceleration acting on the object undergoing uniform circular motion is called centripetal acceleration.
• It always acts on the object along the radius towards the center of the circular path.
• The magnitude of centripetal acceleration,

\(a = \frac{{{v^2}}}{r}\)

Where v = velocity of the object and r = radius

Tangential acceleration (a_t):

• It acts along the tangent to the circular path in the plane of the circular path.
• Mathematically Tangential acceleration is written as

\(\overrightarrow {{a_t}} = \vec \alpha \times \vec r \)

Where α = angular acceleration and r = radius

CALCULATION:

Given – v = 10 m/s, r = 25 m and a_t = 3 m/s²

• Net acceleration is the resultant acceleration of centripetal acceleration and tangential acceleration i.e.,

\(a = \sqrt {a_c^2 + a_t^2} \)

Centripetal Acceleration (a_c):

\(\therefore {a_c} = \frac{{{v^2}}}{r}\)

\( \Rightarrow {a_c} = \frac{{{{\left( {10} \right)}^2}}}{{25}} = \frac{{100}}{{25}} = 4\;m/{s^2}\)

Hence, net acceleration 

Given

Distance1 = 15 km, Speed1 = 30 km/h

Distance2 = 25 km, Speed2 = 10 km/h

Formula Used:

Speed = Distance/Time

Average speed = Total distance/Total time

Calculation:

According to the question,

Total distance = 15 + 25 = 40 km

Total time = 15/30 + 25/10

⇒ (15 + 75)/30 = 90/30 = 3 hours

Average speed = 40/3 km/h

∴ The average speed for the entire journey is 40/3 km/h.

Given 

D₁ = 15 km, S₁ = 30 km/h

D₂ = 25 km, S₂ = 10 km/h

Formula Used:

Average speed = \(\frac{{{D_1} + {D_2}}}{{\frac{{{D_1}}}{{{S_1}}} + \frac{{{D_2}}}{{{S_2}}}}}\)

Calculation:

Average speed for the entire journey = \(\frac{{15 + 25}}{{\frac{{15}}{{30}} + \frac{{25}}{{10}}}}\)

\(= \frac{{40}}{{0.5 + 2.5}}\)

Concept: 

Consider an object's travel distance (D) in time (t).

In that case,

The velocity (v) of the object is given by,

\(v = \frac {D}{t}\)

SI unit of speed is m/sec.

If the quantity is not given in the SI system.

Conversion between km/h and m/sec.

m/sec \(= \frac{km}{h} × \frac{1000}{3600} = \frac{km}{h}× \frac {5}{18}\)

Calculation:

Given data,

Length of train = 100 m

Length of bridge = 1 km = 1000 m

The distance covered by the train to cross the bridge will be the sum of the length of the bridge and the length of the train.

Hence, D = length of train + length of bridge

⇒ D = 100 m + 1000 m = 1100 m

we have velocity (v) = 60 km/h From above concept,

Velocity in m/sec will be given by.

v = 60 × \(\frac{5}{18} \)= \(\frac{300}{18}\) m/s

Hence,

Time (t) = \(\frac {D}{v} = \frac{1100}{\frac{300}{18}}\) = 66 sec

The correct answer is Velocity

Key Points

• A vector quantity is specified by its magnitude as well as the direction associated with it.
  • For example: - Acceleration, velocity, displacement, and angular velocity.
• Velocity is defined as a vector measurement of the rate and direction of motion of an object.
  • velocity formula when an object moving in a straight line: r = d / t
    • r is the rate or speed, d is the distance moved, t is the time it takes to complete the movement.
  • SI unit: meter/second.
  • Other units: mph, ft/s, Km/h.

Additional Information

Given

Distance1 = 15 km, Speed1 = 30 km/h

Distance2 = 25 km, Speed2 = 10 km/h

Formula Used:

Speed = Distance/Time

Average speed = Total distance/Total time

Calculation:

According to the question,

Total distance = 15 + 25 = 40 km

Total time = 15/30 + 25/10

⇒ (15 + 75)/30 = 90/30 = 3 hours

Average speed = 40/3 km/h

∴ The average speed for the entire journey is 40/3 km/h.

Given 

D₁ = 15 km, S₁ = 30 km/h

D₂ = 25 km, S₂ = 10 km/h

Formula Used:

Average speed = \(\frac{{{D_1} + {D_2}}}{{\frac{{{D_1}}}{{{S_1}}} + \frac{{{D_2}}}{{{S_2}}}}}\)

Calculation:

Average speed for the entire journey = \(\frac{{15 + 25}}{{\frac{{15}}{{30}} + \frac{{25}}{{10}}}}\)

\(= \frac{{40}}{{0.5 + 2.5}}\)

Concept:

The equation of motions are:

v = u + at 

v² = u² + 2as                

\(s = ut + \frac{1}{2}a{t^2}\)

S = Distance travelled by the body (m), u = Initial velocity (m/s)

a = Acceleration (m/s²), t = Time taken (sec)

Calculation:

Given:

Mass of body (m) = 40 kg, Acceleration (a) = 5 m/s², Time (t) = 20 s.

According to the kinematics equation, assuming acceleration is constant,

\(S = ut + \frac{1}{2}a{t^2}\)

As the body starts from rest u = 0 i.e. Initial velocity.

\(S = 0 + \frac{1}{2} \times 5 \times {20^2} = 1000\:m\)

∴ S = 1000 metres

CONCEPT:

Centripetal Acceleration (a_c): 

• Acceleration acting on the object undergoing uniform circular motion is called centripetal acceleration.
• It always acts on the object along the radius towards the center of the circular path.
• The magnitude of centripetal acceleration,

\(a = \frac{{{v^2}}}{r}\)

Where v = velocity of the object and r = radius

Tangential acceleration (a_t):

• It acts along the tangent to the circular path in the plane of the circular path.
• Mathematically Tangential acceleration is written as

\(\overrightarrow {{a_t}} = \vec \alpha \times \vec r \)

Where α = angular acceleration and r = radius

CALCULATION:

Given – v = 10 m/s, r = 25 m and a_t = 3 m/s²

• Net acceleration is the resultant acceleration of centripetal acceleration and tangential acceleration i.e.,

\(a = \sqrt {a_c^2 + a_t^2} \)

Centripetal Acceleration (a_c):

\(\therefore {a_c} = \frac{{{v^2}}}{r}\)

\( \Rightarrow {a_c} = \frac{{{{\left( {10} \right)}^2}}}{{25}} = \frac{{100}}{{25}} = 4\;m/{s^2}\)

Hence, net acceleration 

The correct answer is Velocity

Key Points

• A vector quantity is specified by its magnitude as well as the direction associated with it.
  • For example: - Acceleration, velocity, displacement, and angular velocity.
• Velocity is defined as a vector measurement of the rate and direction of motion of an object.
  • velocity formula when an object moving in a straight line: r = d / t
    • r is the rate or speed, d is the distance moved, t is the time it takes to complete the movement.
  • SI unit: meter/second.
  • Other units: mph, ft/s, Km/h.

Additional Information

Explanation:

• The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
• The acceleration in a body is due to an unbalanced force, this can be explained by the first two of Newton's laws of motion
• According to Newton's first law of motion, an object continues to be in a state of rest or of motion until an external and unbalanced force is applied to it
• According to Newton's second law of motion, the force is equal to the change in the rate of momentum, that is,

Initial momentum = mu

Final momentum = mv

Force = Change in the rate of momentum given by:

\(F=\frac{mv-mu}{t}=m(\frac{v-u}{t})=ma\)

Here, m is the mass of the object

u is the initial velocity is the velocity after time t

a is the acceleration

Therefore, acceleration in the body is due to the unbalanced force.

Odometer is to mileage as compass is to the direction.

Odometer:

• It is an instrument used to measure the distance travelled by a wheeled vehicle
• The function is to calculate the mileage or the total distance

Compass:

• It is an instrument used for navigation purposes.
• The main function is to determine the direction and orientation of an object or a person from the north.
• A compass rose is used to show the directions and a needle is used to show the actual direction of the moving object.

Explanation: The statement given in the question is talking about the function of an odometer that is to measure milage. So the function of the compass is to understand the direction of an object. The needle is used in a compass to indicate the actual direction.

Speed: It is the rate at which an object or person is moving in a unit of time.

Hiking: It is an activity for pleasure time or exercise. When people go for a long distance to spend his/her pleasure time or exercise it is called hiking.

Needle: It is a fine piece of metal that has a sharp end.

The correct answer is the average speed.

Key Points

• Speed is the scalar measure of the rate of movement of a body expressed either as the distance traveled divided by the time taken.
• Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
• Displacement is a vector quantity that refers to "how far out of place an object is".
  • It is the object's overall change in position.
• Average speed is the average of all instantaneous speeds. It is found simply by a distance/time ratio.
• Velocity is defined as a vector measurement of the rate and direction of motion of an object.
  • Velocity formula when an object moving in a straight line: r = d / t.
    • r is the rate or speed, d is the distance moved, t is the time it takes to complete the movement.
• A body moving with a constant speed has velocity without acceleration.

Concept:

From Newton's Second Law of motion

F = ma

and distance traveled S 

\(s = ut + \frac{1}{2}a{t^2}\)

Claculation:

Given: m = 5 kg, F= 12 N, t = 2s

a = F/m = 12/5 = 2.4 m/s²

Here u = 0 (body is at rest)

\(s = 0 + \frac{1}{2} \times 2.4 \times {2^2} = 4.8\;m\)

Speed of a car = 20 × 18/5 = 72 km/hour

⇒ In 1 hour = 72 km

⇒ In 2.5 hours = 72 × 2.5 = 180 km

The correct answer is metre per second (m/s).Key Points

• The basic unit of speed of an object is metre per second (m/s).
• The speed of an object is defined as the rate at which it covers a distance in a given time.
• It is used to express the speed of objects that move relatively faster than the speed of light.

Additional Information

• Metre per km (m/km) is not a standard unit of speed.
• Metre per hour (m/h) is a unit of speed but it is not the basic unit of speed.
  • It is used to express the speed of objects that move relatively slower than the speed of light.
• Metre per minute (m/m) is also not the basic unit of speed.
  • It is used to express the speed of objects that move relatively slower than the speed of light.