Question

describe three types of changes in velocity.
what is the equation for acceleration?
what shows acceleration on a speed-time graph?
define instantaneous acceleration.

Answer 1

1) Three types of changes in velocity
- Change in speed (magnitude only): the object speeds up (positive acceleration) or slows down (negative acceleration/deceleration).
- Change in direction (direction only): speed can stay constant while direction changes (e.g., uniform circular motion) — velocity changes because it is a vector.
- Change in both speed and direction: both the magnitude and direction of the velocity vector change (e.g., a car turning while accelerating).

2) Equation for acceleration
- Average acceleration: a_avg = Δv / Δt = (v_final − v_initial) / (t_final − t_initial).
- Instantaneous acceleration: a(t) = dv/dt (the time derivative of velocity).
(SI unit: metres per second squared, m/s^2.)

3) What shows acceleration on a speed–time graph
- Acceleration is the gradient (slope) of the speed–time graph.
- Positive slope → speeding up (positive acceleration).
- Negative slope → slowing down (negative acceleration).
- Zero slope (horizontal line) → zero acceleration (constant speed).
- A curved speed–time line means acceleration is changing with time (non-constant); the instantaneous acceleration is the slope of the tangent at the point.

4) Definition of instantaneous acceleration
- Instantaneous acceleration is the acceleration at a specific instant: the limit of the average acceleration as the time interval approaches zero, mathematically a(t) = dv/dt.