Question

Plz i need help for the 5 problems. plz show the work!!!

1. A car starts from rest and, after 10s, it is moving at 30 m/s. Calculate the acceleration.


2. A truck is moving initially at 10 m/s and, after 8s, it reaches a final velocity of 22 m/s. Calculate the acceleration.


3. A car accelerates at 5 m/s^2. Assuming the car starts from rest, how much time does it need to accelerate to a speed of 15 m/s?


4. A car is moving with a constant velocity of 20 m/s for 10 seconds. What is its acceleration?


5. A shuttle bus comes to a sudden stop by applying the brake, it accelerates uniformly at -4.1 m/s^2 and it slows from 9.0 m/s to 0.0 m/s. Find the time interval of the acceleration of the bus.

Answer 1

1. 3
`m/s^(2)`

2. 1.5
`m/s^(2)`

3. 3 seconds

4. 0
`m/s^(2)`

5. 2.2 seconds

Step-by-step explanation:

(1)

From v= u + at where v is final velocity, u is initial velocity, a is acceleration and t is time.

Making a the subject we have

`a=\frac {v-u}{t}`

Substituting u=0 since it’s at rest, v=30m/s and t=10 seconds

a =
`\frac {30-0}{10}=3 m/s^(2)`

(2)

From v= u + at where v is final velocity, u is initial velocity, a is acceleration and t is time.

Making a the subject we have

`a=\frac {v-u}{t}`

Substituting u=10m/s, v=22m/s and t=8 seconds

a =
`\frac {22-10}{8}=1.5 m/s^(2)`

(3)

From v= u + at where v is final velocity, u is initial velocity, a is acceleration and t is time.

Making t the subject we have

`t=\frac {v-u}{a}`

Substituting u=0m/s since at rest, v=15m/s and a=5
`\frac {m}{s^(2)}`

=
`\frac {15-0}{5}=3s`

(4)

When initial and final velocity are constant, there’s no acceleration as proven below

From v= u + at where v is final velocity, u is initial velocity, a is acceleration and t is time.

Making a the subject we have

`a=\frac {v-u}{t}`

Substituting u=20 since it’s at rest, v=20m/s and t=10 seconds

a =
`\frac {20-20}{10}=0 m/s^(2)`

(5)

From v= u + at where v is final velocity, u is initial velocity, a is acceleration and t is time.

Making t the subject we have

`t=\frac {v-u}{a}`

Substituting u=9m/s since at rest, v=0m/s and a=-4.1
`\frac {m}{s^(2)}`

=
`\frac {0-9}{-4.1}=2.2s`