Question

1. A car speeds up with an acceleration of 2m/s 2 over 10s. If the car had an

initial velocity of 10m/s, how far did it travel?

Answer 1

Using the kinematic equation for uniformly accelerated motion, the car with an initial velocity of 10 m/s and an acceleration of 2 m/s2 for 10 seconds traveled a total distance of 200 meters.

Step-by-step explanation:

The student has asked about the distance a car travels after accelerating from an initial velocity with a constant acceleration over a certain time period. To find this distance, we can use the kinematic equation for uniformly accelerated motion, which is:

d = v_i \( t \) + \(1/2 \)a \( t^2 \)

where d is the distance traveled, v_i is the initial velocity, t is the time period, and a is the acceleration. Given that the initial velocity v_i is 10 m/s, the acceleration a is 2 m/s2, and the time t is 10 seconds, we can compute the distance:

d = (10 m/s) \( 10 s \) + \(1/2 \)(2 m/s2) \( (10 s)2 \)

d = 100 m + 100 m

d = 200 m

Thus, the car traveled a distance of 200 meters after speeding up with an acceleration of 2 m/s2 over 10 seconds.