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Motion, Forces and Energy

Distance-Time and Speed-Time Graphs

Cambridge IGCSE Physics

Reading the shape

Distance Time At rest Constant speed Accelerating Decelerating
Distance-time graph shapes.
Speed Time Accelerating Constant speed Decelerating
Speed-time graph shapes.
GraphShapeMotion
distance-timehorizontal lineat rest
distance-timestraight line sloping upconstant speed
distance-timecurve getting steeperspeed increases
distance-timecurve getting less steepspeed decreases
speed-timehorizontal lineconstant speed
speed-timeline sloping upaccelerates
speed-timeline sloping downdecelerates
speed-timeline on the time axisat rest
  • A steeper distance-time line: a greater speed.
  • Sketching a speed-time graph: constant speed is a straight horizontal line; slowing at a steady rate to rest is a straight line with a negative gradient meeting the time axis.
Speed-time shapeMotion
straight line sloping upconstant acceleration
straight line sloping downconstant deceleration
curve getting steeperincreasing acceleration
curve getting less steepdecreasing acceleration

Gradient

Speed = gradient of a straight-line section of a distance-time graph = change in distance / change in time.

  • Acceleration = gradient of a speed-time graph = change in speed / change in time.
  • On a curve: draw the tangent at that time, then use two points on the tangent: a = gradient of tangent.

Area under a speed-time graph

  • Distance travelled = area under the speed-time graph.
  • Constant speed: a rectangle, speed × time. Constant acceleration from rest: a triangle, ½ × base × height. Otherwise split the area into rectangles and triangles and add them.

Free fall

Near the surface of the Earth the acceleration of free fall g is approximately constant and approximately 9.8 m/s2.

Falling with and without air resistance

  • Without air resistance: an object falls with a constant acceleration g, a straight line on a speed-time graph.
  • Through a liquid, the liquid resistance acts as air resistance does below.

Reaching terminal velocity

  1. At the start the only force is the weight, so the object accelerates at 9.8 m/s2 initially.
  2. Air resistance increases as speed increases.
  3. The resultant force decreases.
  4. The acceleration decreases.
  5. When the air resistance is equal to the weight, the resultant force is zero and the acceleration is zero.
  6. The object falls at terminal velocity, a constant speed.
Speed Time Terminal velocity Gradient decreasing
Falling with air resistance: the gradient decreases to zero at terminal velocity.

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