Question

1. A car is traveling at 28 meters per second north; 10 seconds later the car is
traveling 15 meters per second north. What is the car’s acceleration?
2. A car with a mass of 2150 kg is traveling at west 70 m/s, two minutes later the car
is traveling west at 100 m/s. What is the car’s acceleration?
3. I have a mass of 500 kg. What force is needed to accelerate me at 1m/s 2 ?
4. A 77 kg man jumps out of a plane. What force does gravity exert on him?
5. A 75 kg person in a frictionless environment throws a 5 kg ball with a force of 15 N.
What is the acceleration of the ball & the person?
6. A store clerk pushes a row of shopping carts through the parking lot, accelerating
them at 1 m/s 2 . If the carts have a mass of 300 kilograms, how much force did the
clerk put on the carts?
7. How much force is required to accelerate a 30 000 kg truck at 5 m/s 2 ?
8. A table is pushed with an applied force of 120 N parallel to the floor. It accelerated
at 8.23 m/s 2 to the right. Neglecting friction, what is the mass of the box?
9. A cabinet is pushed with an applied force of 80 N parallel to the floor. It
accelerated at 5.90 m/s 2 to the right. Neglecting friction, what is the mass of the
box?
10. A crate is pushed with an applied force of 30 N parallel to the floor. It accelerated
at 2.70 m/s 2 to the right. Neglecting friction, what is the mass of the box?

Answer 1

Answer:

Velocity: Acceleration and Newton's 3 laws: A car is traveling at 28 meters per second north; 10 seconds

Answer 2

Given:

1. Initial velocity of car = 28m/s

Final velocity of car = 15m/s

Time during which the car decelerates = 10s

2. Mass of car = 2150kg

Initial velocity of car = 70m/s

Final velocity of car = 100m/s

Time during which the car accelerates = 2minutes

3. Mass = 500kg

Acceleration= 1m/s²

4. Mass of man = 77kg

Acceleration due to gravity, g = 9.8m/s²

5. Mass of man = 75kg

Mass of ball = 5kg

The force with which he throws = 15N

6. Acceleration of carts = 1m/s²

Mass of carts = 300kg

7. Mass of truck = 30000kg

Acceleration of truck = 5m/s²

8. Force applied on table = 120N

Acceleration = 8.23m/s²

9. Force applied on cabinet = 80N

Acceleration = 5.90m/s²

10. Force applied on crate = 30N

Acceleration = 2.70m/s²

To find:

1. Acceleration of the car.

2. Acceleration of the car.

3. Force needed to accelerate.

4. Force exerted by gravity on man.

5. Acceleration of the ball and the person.

6. Force applied by the clerk onto the carts.

7. Force required to accelerate the truck.

8. Mass of the table.

9. Mass of the cabinet.

10. Mass of the crate.

Solution:

1. Acceleration is the rate of change of velocity of an object with time.

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

where, $a,v,u,t$ are acceleration, final velocity, initial velocity and time during which the object is accelerated respectively. Here, the speed decreases from 28m/s to 15m/s. Hence, the car is decelerating. Therefore, the sign of acceleration will be negative.

$a=\frac{15-28}{10}=\frac{-13}{10}=-1.3m/s^{2}$

2. Here, time is given in minutes whereas the velocity is expressed in m/s. Hence, converting minutes into seconds.

$1min=60s$

$2min=2*60=120s$

$a=\frac{v-u}{t}=\frac{100-70}{120}=\frac{30}{120}=0.25m/s^{2}$

3. When a force $F$ is applied to a body and it moves with a velocity $v$, the rate of change of velocity of the body is proportional to the force applied and moves in the direction of the force applied. This is given by:

$F=ma$

Here, $m=500kg, a=1m/s^{2}$

∴ $F=500*1=500N$

4. The acceleration due to gravity experienced by the man is given by $g=9.8m/s^{2}$

$F=mg=77*9.8=754.6N$

5. Acceleration of the ball with mass 5kg is given by:

$F=ma$

$a=\frac{F}{m}=\frac{15}{5} =3m/s^{2}$

Acceleration of the person is given by:

$a=\frac{F}{m}=\frac{15}{75}=0.2m/s^{2}$

6. The force exerted by the clerk on the carts is given by:

$F=ma=300*1=300N$

7. The force required to accelerate the truck is given by:

$m=30000kg,a=5m/s^{2}$

$F=ma=30000*5=150000N$

8. Mass of the table which is pushed by a force of 120N is given by:

$F=ma$

$m=\frac{F}{a}=\frac{120}{8.23}=14.6kg$

9. Mass of the cabinet which is pushed by a force of 80N is given by:

$m=\frac{F}{a}=\frac{80}{5.90}=13.5kg$

10. Mass of the crate which is pushed by a force of 30N is given by:

$m=\frac{F}{a}=\frac{30}{2.70}=11.11 kg$

The following are the answers:

1. The acceleration of the car is -1.3m/s².

2. The acceleration of the car is 0.2m/s².

3. The force needed by me is 500N.

4. The force exerted by gravity on man is 754.6N.

5. Acceleration of the ball and man is 3m/s² and 0.2m/s² respectively.

6. The force exerted by the clerk on the carts is 300N.

7. Force required by the truck to accelerate 150000N.

8. Mass of the table is 14.6kg.

9. Mass of the cabinet is 13.5kg.

10. Mass of the crate is 11.11kg.