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# Speed and velocity for OCR A-level Physics

1. Speed and velocity
2. Speed from graphs
3. Angular velocity

Speed is the amount of distance covered by an object per unit time. It is calculated by dividing the distance travelled by the time taken. The standard units of speed are metres per second (m/s). Speed is a scalar quantity, since it is only described by magnitude. When the motion of an object is non-uniform, ie. it is not travelling at a constant speed, the average speed can be calculated by dividing the total distance travelled by the total time taken.

Velocity is the speed of an object in a given direction, thus velocity is a vector quantity. Velocity has the same standard units as speed, m/s. Velocity-time graphs can be drawn to model the motion of an object. If the velocity of an object is changing, the velocity value on the graph decreases or increases. A horizontal line in the velocity-time graph indicates that the velocity is not changing.

The motion of an object in a straight line can be modelled using a distance-time graph. The gradient of a distance-time graph at a specific point in time is the speed of the object at that time. The speed of an object from a straight line in a distance-time graph can be found by dividing the change of distance by the in time between two points. An accelerating object can be modelled on distance-time graph using curved lines.

One of the units for measuring angles is radians. ฯ radians is equivalent to 180ยฐ. An angle in degress can be converted to radians by dividing it by 180 and multiplying by ฯ. Radians are typically used in calculations involving circular motion.

Angular displacement is the change in angle that an object travels through when travelling through a circle. It is calculated by dividing the distance travelled in the circle by the radius of the circle and is given in radians.

Angular velocity is the change in angular displacement per unit time. Its units are rad/s. Angular velocity can be calculated by dividing the angular displacement by the change in time. This is equivalent to dividing 2ฯ by the time period, which is the time taken for the object to complete one rotation of the circle, or by 2ฯf, where f is the frequency of the object, ie. the number of rotations per second.

Angular velocity can be related to the linear speed at which the object is travelling around the circle. Angular velocity can be calculated by dividing the linear speed by the radius of the circle through which the object is travelling.

# 1

Rebecca lives 550 m away from her school. Given that Rebecca walks to school in 6 minutes, calculate the average speed of her motion.

6 minutes = 360 seconds
speed = distance รท time
speed = 550 m รท 360 s = 1.53 m/s (to 3 sf)

1.53 m/s

# 2

An object is travelling at a constant speed for 15 seconds, during which it travels through 7 m. The object is then stationary for 5 seconds, and finally accelerates for another 10 seconds, reaching 20 m at the end of its journey. Sketch a distance-time graph to model this journey.

In the first 15 seconds, the object is moving at a constant speed, therefore the gradient of the graph is positive and constant. In the next 5 seconds, the object is stationary, therefore the graph is flat. In the last 10 seconds, the object is accelerating, therefore the gradient is increasing.

image

# 3

Fatima is playing with a fidget spinner of radius 4 cm. Given that it has a linear speed of 9 m/s, calculate the time period of the fidget spinner.

ฯ = v รท r
ฯ = 9 รท 0.4 = 22.5 rad/s

ฯ = 2ฯ รท T
22.5 = 2ฯ รท T
T = 0.279 s (to 3sf)

0.279 s

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