Question

A race car accelerates uniformly from 19.5 m/s to 50.1 m/s in 2.47 seconds. Determine
the acceleration of the car and the distance traveled.

Answer 1

Answer:

12.4m/s²; 80.99m

Explanation:

Acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time. Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

$Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}$

Given the following data;

Initial velocity = 19.5m/s

Final velocity = 50.1m/s

Time = 2.47 secs

Substituting into the equation;

$a = \frac{50.1 - 19.5}{2.47}$

$a = \frac{30.6}{2.47}$

Acceleration, a = 12.4m/s²

Solving for the distance covered;

$S = ut + \frac {1}{2}at^{2}$

Substituting into the values into the equation;

$S = 19.5(2.47) + \frac {1}{2}(12.4)(2.47)^{2}$

$S = 48.165 + 6.2 *6.1009$

$S = 48.165 + 32.8256$

S = 80.99m