Physics Question!

Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead (from rest) with a constant acceleration of 1.3 m/s². At the same instant, a truck traveling with a constant speed of 38.7 mph passes the car.

(a)How much time in seconds does it take the car to catch up with the truck? Keep 2 decimal places.

(b) How far in meters beyond its starting point does the car catch up with the truck? Keep 2 decimal places

(c) How fast in m/s is the car traveling when it catches up with the truck?

Thank you

Answer 1

Watch out for the trap here---we are given acceleration in meters / second² , and velocity in miles per hour, so we have to get everything in the same units

We can start with the equation for distance traveled at a constant acceleration:

For the car accelerating:

d = 1/2 * a * t²

With an acceleration of 1.3 m/s²:

d = 0.65 * t²

For the truck, the distance is simply d =v * t, so

v = 38.7 miles / hour * 1.609 km/mile * 1000 m/km * 1 hour / 3600 s = 17.30 m/s

d = 17.3 * t

Set the 2 equations for d equal to each other:

0.65 * t² = 17.3 * t

t = 17.3 / 0.65 = 29.61 seconds

Use either equation to solve for the distance, and then v = d/t to get the velocity