[3.] While driving on the highway at a constant speed v0, significantly above th

Question

[3.] While driving on the highway at a constant speed v0, significantly above the speed limit, you pass in front of a parked police car without noticing it. After a few seconds, during which time you have moved a distance d, the police car starts chasing you with a constant acceleration a0. Give your answers in terms of v0, d, and a0 and check the units of your answers. Assuming that you keep moving at a constant speed, and that the highway can be considered straight: [a] How long will it take for the police car to reach you? [b] How far has the police car traveled when it reaches you? [c] What is the speed of the police car when it reaches you?

Explanation / Answer

Given,

You -
Initial Speed = v0
Acceleration = 0

Police -
Initial Speed = 0
Acceleration = a0

Distance between you & Police = d

(a)
Let time taken by Police to Catch = t

Now,
Distance travelled by Police in this time is given by Formula
S = u*t + 1/2 * at^2
Sp = 0 + 1/2 * a0*t^2
Sp = 1/2 * a0*t^2

Distance travelled by you in the Given time,
S = u*t + 1/2 * at^2
Sy = v0*t + 0
Sy = v0*t

Now, as police catches you in this time, we can say
Sp = Sy + d
Subsituing Values -
1/2 * a0*t^2 = v0*t + d

1/2 * a0*t^2 - v0*t = d
t * (1/2 * a0*t - v0) = d

t = d , (2*(d+v0))/a0
Time taken by Police car to reach, t = (2*(d+v0))/a0

(b)
Distance travelled by Police,
Sp = 1/2 * a0*t^2
Sp = 1/2 * a0 *((2*(d+v0))/a0)^2
Sp = 2*(d+v0)^2 /a0

(c)
Speed of the police car when it reaches you,
V = u + a*t
V = 0 + a0 * (2*(d+v0))/a0
V = 2*(d+v0)

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.