What is the nature of velocity-time graph for a car moving with uniform acceleration?

Concept:

• Acceleration is defined as the rate of change of velocity with respect to time.
• It is a vector quantity since it has both direction and magnitude
• \(a = \frac{dv}{dt}\)
• Where, a = acceleration, dv = change in velocity, dt = change in time.
• SI unit of acceleration is m/s²

Calculation:

For a uniform acceleration, \(\frac{dv}{dt} = constant\)

⇒ dv = constant × dt

Integrating both sides, we get

⇒ v = constant × t

⇒ v ∝ t, this equation gives a graph of a straight line.

Additional InformationDifferent types of acceleration 

• Uniform and Non-Uniform Acceleration
  • If an equal amount of velocity increases in equal intervals of time, then the object is said to be in uniform acceleration.
  • If the velocity of the object changes by unequal amounts in equal intervals of time, the object is said to be non-uniform acceleration.
• ​Average Acceleration is the change in velocity for a particular specified time interval. It is the total change in velocity in the given interval divided by the total time taken for the change. 
• Instantaneous acceleration is the ratio of change in velocity during a given time interval such that the time interval goes to zero.