At the instant the traffic light turns green, an automobile starts with a consta

Question

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s^2. At the same instant a truck, traveling with a constant speed of 9.S m/s overtakes and passes the automobile. How far beyond the traffic signal will the automobile overtake the truck? How fast will the automobile be traveling at that instant? You are to drive to an interview in another town a distance of 400 km away on 1-75. The interview is scheduled for 12:15 PM. You plan to drive at 100 km/h, so you leave at 8:00 AM to allow for extra time. You drive at 100 km/h for the first 200 km, but construction work forces you to slow to 60 km/h for the next 60 km. What would be your least speed needed for the rest of the trip to arrive on time for the interview?

Explanation / Answer

3)
For Automobile.
Initial speed, u = 0
a = 2.2 m/s^2

For Truck,
v = 9.5 m/s

Let it catches x m far beyond the traffic signal.
Let time taken to reach there = t

So,
Distance travelled by Truck, x = 9.5*t
Distance travelled by car, x = 0 + 1/2*2.2*t^2 = 1.1 * t^2

9.5 * t =  1.1 * t^2
t = 8.64 s

Distance far beyond the traffic signal, = 9.5 * 8.64 = 82.1 m

(b)
Speed of automobile,
v = u + a*t
v = 2.2 * 8.64
v = 19.0 m/s
Speed of automobile,v = 19.0 m/s

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