Question

A motorist traveling with a constant speed of 15m/s passes a school-crossing corner, where the speed limit is 10m/s. Just as the motorist passes, a police officer on a motorcycle at the corner starts off in pursuit with constant acceleration of 3m/s^2. (a)How much time elapses before the police catches up the motorist? (b)What is the officer's speed limit at that point? (c)What is the total distance each vehicle has traveled at that point?

Answer 1

Answer:

a) 10 seconds

b) 30 m/s

c) 150 m

Step-by-step explanation:

Given:

Speed of the motorist, v = 15 m/s

speed limit = 10 m/s

acceleration of the police officer = 3 m/s²

Now,

The police officer will catch the motorist, when the distance traveled by both will be equal

let, t be the time taken to catch

therefore,

For motorist,

Distance = speed × time

= 15 × t

and for officer

Distance = $ut + \frac{1}{2}at^2$

= 0 × t + 0.5 × 3 × t²

= 1.5t²

since the distance will be equal

therefore,

15 × t = 1.5t²

or

a) t = 10 seconds

b) officer's speed, V = u + at

= 0 + 3 × 10

= 30 m/s

c) distance traveled = speed × time

= 15 × 10

= 150 m

So the distance traveled is 150 m