# StudySquare

This page covers the following topics:

1. Newton’s second law

2. Acceleration

3. Deceleration

4. Interpreting velocity-time graphs

5. Gradient of velocity-time graphs

6. Gravity

Newton's second law states that the acceleration of an object is directly proportional to the resultant force in its direction and is inversely proportional to the mass of the object. It can be expressed using the following formula: resultant force = mass × acceleration. This equation can only be used when the acceleration of the moving object is constant.

Acceleration is the rate of change of velocity of an object. It is a vector quantity, as it is expressed by both magnitude and direction. It can be calculated using the following equation: acceleration = change in velocity ÷ time.

Deceleration is negative acceleration. It is calculated using the same equation as acceleration. A positive deceleration is a negative acceleration, with an example being a slowing down object.

A velocity-time graph is a graphical representation of an object's motion over a given period of time. The direction and the speed of an object can be deduced from the velocity-time graph of its motion. The area under the velocity-time graph of an object's motion gives its displacement.

The gradient of a velocity-time graph gives the acceleration of an object. A positive gradient shows that the object is accelerating, whereas a negative one shows that it is decelerating.

Objects with mass have a gravitational field around them and thus they experience a pulling force. This is the force caused by gravity. The Earth's gravitational field strength is approximately 10 m/s², and thus for every kg of mass of an object, it experiences a force of 10 N caused by gravity.

When objects are falling near the surface of the Earth, the Earth's gravitational field exerts a pulling force on the object. This causes a resultant force to act on the object, and thus, by Newton's second law, the falling object accelerates towards the surface of the Earth due to gravity. This force is also called the weight and it can be calculated using the following formula: weight = mass × gravitational field strength.

# 1

Explain why objects near the surface of the Earth accelerate towards it.

These objects are in the graviational field of the Earth and thus experience a pull of gravity from the Earth. This pulling force causes a resultant force to act on the falling object and thus, by Newton's second law, the object accelerates in the direction of the force, ie. towards the surface of the Earth.

gravitational field → gravitational pull → resultant force → acceleration towards the Earth

# 2

The velocity-time graph of an object's motion is drawn as a horizontal line. Explain what this says about the object's motion.

The object is travelling at constant velocity.

constant velocity

# 3

A car moving at a velocity of 30 m/s slows down to 18 m/s in 9 seconds. Calculate the deceleration of the car to 3 significant figures.

a = (v − u)/t

a = (18 m/s − 30 m/s)/9 s = −1.33 m/s² (to 3 significant figures)

Therefore, the deceleration of the object is 1.33 m/s².

1.33 m/s²

# 4

An object is travelling at a constant velocity of 15 m/s for the first 6 seconds of its motion and then it slows down at a constant rate to rest in a further 5 seconds. Draw a velocity-time graph for this object.

The y axis of the graph is velocity in m/s and the x axis is time in seconds.

The object travels at a 15 m/s velocity for 6 seconds.

The object then decelerates to rest in a further 5 seconds.

image

# 5

A car is travelling in a straight line at a constant velocity of 10 m/s when it starts to accelerate. After 5 seconds, the velocity of the car is 14 m/s. Calculate the magnitude of the acceleration of the car.

a = (v − u) ÷ t

acceleration = (14 m/s − 10 m/s) ÷ 5 s = 0.8 m/s²

0.8 m/s²

End of page