Speed, Velocity, and Acceleration

Physics NotesGCE Study buddy

Displacement The distance in a straight line in a certain direction from

the starting point Eg Lily walked 1km to the North, then 2km to the East

followed by 1km to the south. a. what is her total walking distance? b. what is her final displacement?

Answers: a. 1 + 2 + 1 = 4km b. 2m due east from starting point

Speed and Velocity Scalar: has only magnitude and no direction

Speed is distance travelled by a body per unit time Vector: has both magnitude and direction

Velocity is distance travelled per unit time in a stated direction

Velocity = Distance/time Units: ms-1 or kmh-1 Average speed is NOT the constant speed average speed = total distance/total time Instantaneous speed: the speed at any instant

Use speedometer to find instantaneous speed Can be found by finding the gradient of the tangent to the

displacement-time graph, at that point in time

Speed measurement using ticker-tape timer

Acceleration Defined as the rate of change of velocity with time Acceleration = (final v - initial v)/time Units: ms-2 or kmh-2 If velocity is constant, acceleration= 0 If velocity decreasing --> negative acceleration/deceleration The gradient of a velocity-time graph of a moving object gives

the acceleration of the object at a given time

Acceleration of bodies falling near to earth An object falling near to Earth, where the air resistance is

negligible, has a velocity-time graph that is s straight line. It falls with a constant acceleration

The only force acting on the object experiencing free fall is the force of gravity

Acceleration = 10ms-2

Acceleration-time graphs

Decreasing acceleration

Decreasing speed

Constant speed

Velocity-time graphs

Increasing acceleration

Constant acceleration

Zero speedConstant speed

Constant speed

Zero acceleration

Distance-time graph

Area under velocity-time graph

Area under velocity-time graph is the distance

Question Time!

5.00.0

6.0

Velocity m/s

Time s

The figure shows the variation of speed v with time t at the beginning of a bicycle ride.a. Describe the variation of the acceleration of the bicycle with timeb. Use the graph to determinei. the speed at t = 5.00sii. the acceleration at t = 5.00siii. the approximate distance travelled in the first 5.00s

Answers

a. The acceleration has an initial positive value which decreases until it reaches 0m/s^2bi. 6.0m/sbii. 0m/s^2biii. distance = area under graph = 0.5 x (5.0+2.5) x 6.0= 22.5m

Question TimeStudents investigating motion down an inclined plane measure the speed of a steel ball at one second intervals after the ball starts to roll down from rest down one such plane a. calculate the average acceleration over the first 3.00sb. calculate the average speed over the first 3.00sc. what was the distance travelled by the ball in the first 3.00s?d. how do the numbers in the table show that the acceleration was constant?

time in s 0.00 1.00 2.00 3.00

speed in m/s

0.00 0.60 1.20 1.80

Answersa. 0.60m/s^2 b. average speed = 0.5 x (u + v) = 0.5 x (0.00 + 1.80) = 0.90m/s c. distance = average speed x time = 0.90 x 3 = 2.7m d. The speed increases by a constant value of 0.60m/s every second, hence the acceleration can be seen to be constant