Question

A car starts at rest and speeds up with an average positive acceleration of 4.0 meters per second squared in a straight line. The car travels a distance of 98 meters in 7.0 seconds. Calculate the car's final velocity.

a) 34 m/s
b) 42 m/s
c) 28 m/s
d) 56 m/s

Answer 1

Using the kinematic equation v^2 = u^2 + 2as, with an initial velocity of 0 m/s, an acceleration of 4.0 m/s^2, and a distance of 98 meters, the car's final velocity is calculated to be 28 m/s.

Step-by-step explanation:

The question asks for the car's final velocity after accelerating for a given time and distance. We are given an initial velocity of 0 m/s (since the car starts at rest), an average acceleration of 4.0 m/s2, and a distance traveled of 98 meters. To find the final velocity, we can use the kinematic equation v2 = u2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

Let's plug in the numbers: v2 = 02 + 2 × (4.0 m/s2) × (98 m). This simplifies to v2 = 2 × 4.0 × 98, which gives us v2 = 784. Taking the square root of both sides, we find that v = 28 m/s. Therefore, the car's final velocity is 28 m/s, which corresponds to option (c).