Question #35678

A speeding car passes a highway patrol checkpoint and then accelerates at a constant rate. 3.15 s later, the car is 240 m from the checkpoint and its speed is then 33.7 m/s. What is the acceleration of the car?

Expert's answer

`[s = 240 m ]`

[V1 - speed at the checkpoint ]

[V2 = 33.7 m/s]

[a - acceleration]

[t = 3.15 s]

s = V1*t + (at^2)/2 (1)

V2 = V1 + at => V1 = V2 - at (2)

(2) -> (1) :

s = (V2-at)t + (at^2)/2 = V2*t - at^2 + (at^2)/2 = V2*t - (at^2)/2 (3)

From (3):

a = 2*(V2*t - s)/(t^2)

a = -27 [ m/(s^2) ]

So, V1 = 118.7 (m/s)

Answer: a = -27 [ m/(s^2) ]

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