## Motion – Solved Problems

### Problem 1. A car covers the 1st half of the distance between two places at a speed of 40 km/hr and the 2nd half at 60 km/hr what is the average speed of the car ?

**Solution. **

Suppose the total distance covered is S. Then time taken to cover first’s distance with speed

40 km/hr.

### Problem 2. An object moving to the right has a decrease in velocity from 5.0 m/s to 1.0 m/s in 2.0 s. What is the average acceleration ? What does your result mean ?

**Solution. **

Given v_{0} = + 5.0 m/s, v = + 1.0 m/s, t = 2.0 s

According to the definition of average acceleration,

The negative sign means the acceleration is opposite to velocity (deceleration). The result means that the object decreases its velocity by 2.0 m/s every s or 2.0 m/s^{2}.

### Problem 3. The table below shows the distance in cm, travelled by the objects *A, B *and *C *during each second.

#### (i) Which object is moving with constant speed ? Give a reason for your answer.

#### (ii) Which object is moving with a constant acceleration ? Give a reason.

#### (iii) Which object is moving with irregular acceleration ?

**Solution**

**Answer (i).**

The object *A *is moving with constant speed. The reason is that it covers equal distance=20cm. in each second,

**Answer (ii).**

The object *C *is moving with a constant acceleration. The reason is that for the object *C, *the distance covered increases by the same amount in each second. It can further be verified by drawing graph between *S *(total distance covered) and *t ^{2} *(square of time taken). The graph will be a straight line.

t^{2} |
1 | 4 | 9 | 16 | 25 |

s |
20 | 80 | 180 | 320 | 500 |

**Answer (iii).**

The object *B *is moving with irregular acceleration.

### Question 4. An automobile accelerates uniformly from rest to 25 m/s while traveling 100m. What is the acceleration of the automobile ?

**Solution.**

Given: v_{0} = 0 (rest), v = 25m/s, *x = *100m. Find a.

Since v^{2} = v_{0}^{2} + 2ax,

Since a is positive, it is in the direction of the velocity or motion.

### Problem 5. car is moving at a speed 50 km/h. Two seconds there after it is moving at 60 km/h. Calculate the acceleration of the car.

**Solution.**

### Problem 6. A bus moving with a velocity of 60 km/h is brought to rest in 20 seconds by applying brakes. Find its acceleration.

**Solution.**

### Problem 7. A bullet moving with 10 m/s hits the wooden plank the bullet is stopped when it penetrates the plank 20 cm. deep, calculate retardation of the bullet.

**Solution. **

### Problem 8. A body with an initial velocity of 18 km/hr accelerates uniformly at the rate of 9 cm s^{-2 }over a distance of 200m. Calculate:

#### (i) the acceleration in ms^{-2}

#### (ii) its final velocity in ms^{-1}

**Solution. (i)**

**Solution (ii)**

### Problem 9. The graph represents the velocity of a particle as a function of time.

#### (a) What is the acceleration at 1.0 s ?

#### (b) What is the acceleration at 3.0 s ?

#### (c) What is the average acceleration between 0 and 5.0 s ?

#### (d) What is the average acceleration for the 8.0 s interval ?

#### (e) What is the displacement for the 8.0 s interval ?

**Solution. (a)**

**Solution (b)**

The slope of the line is zero and a = 0.

**Solution (c)**

**Solution (d) **

**Solution (e) **