0.2 Motion in one dimension  (Page 7/16)

Acceleration

Acceleration

Acceleration is the rate of change of velocity.

Acceleration (symbol $a$ ) is the rate of change of velocity. It is a measure of how fast the velocity of an object changes in time. If we have a change in velocity ( $\Delta v$ ) over a time interval ( $\Delta t$ ), then the acceleration ( $a$ ) is defined as:

Since velocity is a vector, acceleration is also a vector. Acceleration does not provide any information about a motion, but only about how the motion changes. It is not possible to tell how fast an object is moving or in which direction from the acceleration.

Like velocity, acceleration can be negative or positive. We see that when the sign of the acceleration and the velocity are the same, the object is speeding up. If both velocity and acceleration are positive, the object is speeding up in a positive direction. If both velocity and acceleration are negative, the object is speeding up in a negative direction. If velocity is positive and acceleration is negative, then the object is slowing down. Similarly, if the velocity is negative and the acceleration is positive the object is slowing down. This is illustrated in the following worked example.

Acceleration

1. An athlete is accelerating uniformly from an initial velocity of 0 m $·$ s ${}^{-1}$ to a final velocity of 4 m $·$ s ${}^{-1}$ in 2 seconds. Calculate his acceleration. Let the direction that the athlete is running in be the positive direction.
   
2. A bus accelerates uniformly from an initial velocity of 15 m $·$ s ${}^{-1}$ to a final velocity of 7 m $·$ s ${}^{-1}$ in 4 seconds. Calculate the acceleration of the bus. Let the direction of motion of the bus be the positive direction.
   
3. An aeroplane accelerates uniformly from an initial velocity of 200 m $·$ s ${}^{-1}$ to a velocity of 100 m $·$ s ${}^{-1}$ in 10 seconds. It then accelerates uniformly to a final velocity of 240 m $·$ s ${}^{-1}$ in 20 seconds. Let the direction of motion of the aeroplane be the positive direction.
   1. Calculate the acceleration of the aeroplane during the first 10 seconds of the motion.
   2. Calculate the acceleration of the aeroplane during the next 14 seconds of its motion.