1. Deceleration is the gradient of the velocity-time graph. Maximum deceleration occurs where the graph is steepest.
2. Identify the section of the graph with the steepest negative slope.
3. Calculate the gradient for this section using: gradient = (change in y) / (change in x) = (change in velocity) / (time taken).
4. Read the velocity and time values from the start and end of this section accurately.
Full Answer
Deceleration is the rate of change of velocity, which is the gradient of the velocity-time graph. The maximum deceleration corresponds to the steepest downward-sloping section of the graph.
Looking at the graph, the steepest section is between t = 650 s and t = 800 s.
- At t₁ = 650 s, the velocity v₁ = 58 m/s.
- At t₂ = 800 s, the velocity v₂ = 20 m/s.
Gradient = (change in velocity) / (change in time) = (v₂ - v₁) / (t₂ - t₁)
Gradient = (20 - 58) / (800 - 650)
Gradient = -38 / 150
Gradient = -0.2533... m/s²
Deceleration is the positive value of this gradient.
Maximum deceleration = 0.253 m/s² (to 3 significant figures).
Common mistakes
✗ Calculating the area instead of the gradient.\n✗ Misreading the values from the axes.\n✗ Choosing the wrong section of the graph (the less steep part).\n✗ Giving the answer as a negative number (acceleration is negative, deceleration is positive).
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