Question

Please Help!!! As well, please try to show work!

Answer 1

Answer:

If we assume that the rate of change of velocity (acceleration) is a constant, then the constant acceleration is given by

Acceleration=Change in velocityChange in time.

More precisely, the constant acceleration a is given by the formula

a=v(t2)−v(t1)t2−t1,

where v(ti) is the velocity at time ti. Since velocity is a vector, so is acceleration.

Example

A particle is moving in a straight line with constant acceleration of 1.5 m/s2. Initially its velocity is 4.5 m/s. Find the velocity of the particle:

after 1 second

after 3 seconds

after t seconds.

Solution

After 1 second, the velocity is 4.5+1.5=6 m/s.

After 3 seconds, the velocity is 4.5+3×1.5=9 m/s.

After t seconds, the velocity is 4.5+1.5t m/s.

Example

A car is travelling at 100 km/h =2509 m/s, and applies its brakes to stop. The acceleration is −10 m/s2. How long does it take for the car to stop?

Solution

After one second, the car's velocity is 2509−10 m/s. After t seconds, its velocity is

v(t)=2509−10t m/s.

The car stops when v(t)=0. Solving this equation gives

2509−10tt=0=259.

The car takes approximately 2.8 seconds to stop.

(In exercise 6, we will find out how far the car travels during this time.)

Explanation: