Question

A car achieves a speed of 40 m/s by undergoing uniform acceleration of 5 m/s2 in 3 s. Find initial speed of the car.

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Answer 1

Answer:

Let’s begin with a particle with an acceleration a(t) is a known function of time. Since the time derivative of the velocity function is acceleration,

  

we can take the indefinite integral of both sides, finding

  

where C1 is a constant of integration. Since

  

, the velocity is given by

  

Similarly, the time derivative of the position function is the velocity function,

  

Thus, we can use the same mathematical manipulations we just used and find

  

where C2 is a second constant of integration.

We can derive the kinematic equations for a constant acceleration using these integrals. With a(t) = a a constant, and doing the integration in (Figure), we find

Answer 2

Hence, The Initial Speed of the Car is 25 m/s.

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