Answer to Question #251350 in Physics for Laxus

Question

5.     

A car starts from rest and accelerates

uniformly over a time of 5.59 seconds for a distance of 150.00 m. Determine the

acceleration of the car.

 

6.     

Rocket-powered sleds are used to test

the human response to acceleration. If a rocket-powered sled is accelerated to

a speed of 360.00 m/s in 2.50 seconds, then what is the acceleration of the

rocket? What is the distance that the sled travels?

Answer 1

5. Using the kinematic equation, obtain:

$$d = \dfrac{at^2}{2}$$

where $d = 150.00m$ is the distance, $t = 5.59s$ is the time, and $a$ is the acceleration. Expressing $a$, obtain:

$$a = \dfrac{2d}{t^2} = \dfrac{2\cdot 150m}{(5.59s)^2} \approx 9.60m/s^2$$

6. By definition of acceleration:

$$a = \dfrac{v-v_0}{t}$$

where $v = 360.00m/s$ is the final speed, $v_0 = 0$ is the initial speed, and $t=2.50s$ is the time. Thus, obtain:

$$a = \dfrac{360m/s-0}{2.50s} = 144m/s^2$$

The distance is determined with the same equation as in 5):

$$d = \dfrac{at^2}{2} = \dfrac{144m/s^2\cdot (2.5s)^2}{2} = 450m$$

Answer. 5) 9.60m/s^2, 6) 144m/s^2 and 450m.