Aself-driving car traveling along a straight section of road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 32.0 m/s. then the vehicle travels for 53.0 s at constant speed until the brakes are applied, stopping the vehicle in a uniform manner in an additional 5.00 s. (a) how long is the self-driving car in motion (in s)? s (b) what is the average velocity of the self-driving car for the motion described? (enter the magnitude in m/s.) m/s

t = 75.4 s

v = 26.9 m/s

Explanation:

Part1 :

v1 = 0 m/s

v2 = 32 m/s

a = 2 m/s2

The time needed to reach the final speed is:

v2 = v1 + a*t

32 = 0 + 2*t

t = 16 s

Part 2:

constant speed of 32 m/s for 53 s

Part 3:

v2 = 32 m/s

v3 = 0 m/s

t = 5 s

The acceleration is negative because the car is stopping:

v3 = v2 + a*t

0 = 32 + a*5

a = - 6.4 m/s

a) The total time the car is in motion is:

total time = 16 + 53 + 6.4 = 75.4 s

b) For the average speed you can calculate the total distance and divide it by the total time for an easier way

Part 1

d = (32+0)/2 * 16 = 256 m

Part 2

d = 32 * 53 = 1696 m

Part 3

d = (32+0)/2 * 5 = 80 m

Average speed:

v = (256 + 1696 + 80)/75.4 = 26.9 m/s