Worksheet: Instantaneous Speed

In this worksheet, we will practice determining the instantaneous speed of an object by using tangents to find the gradient at a point on the object's distance-time graph.

Q1:

An object moves along a straight line. On the graph, the blue line shows the displacement, 𝑑 , of the object from its starting position over time, 𝑡 .

Which of the three dashed lines is a tangent to the blue line at 𝑡 = 4 s?

  • AThe red line
  • BThe purple line
  • CThe orange line

Which of the three dashed lines is a tangent to the blue line at 𝑡 = 1 s?

  • AThe red line
  • BThe purple line
  • CThe orange line

Which of the three dashed lines is a tangent to the blue line at 𝑡 = 1 6 s?

  • AThe orange line
  • BThe purple line
  • CThe red line

Q2:

An object moves along a straight line. On the graph, the blue line shows the displacement, 𝑑 , of the object from its starting position over time, 𝑡 .

Which of the three dashed lines is a tangent to the blue line at 𝑡 = 4 s?

  • AThe red line
  • BThe orange line
  • CThe purple line

Q3:

A ball is thrown up in the air, and it falls back down to the ground. The height, , of the ball above the ground over time, 𝑡 , is shown on the graph by the blue line. The red line is a tangent to the blue line at 𝑡 = 1 s. What is the speed of the ball at 𝑡 = 1 s?

Q4:

The graph shows the displacement of a motorcycle in a race along a straight track. At which of the labeled points on the graph does the motorcycle have the greatest speed?

  • APoint 𝐴
  • BPoint 𝐶
  • CPoint 𝐵
  • DPoint 𝐸
  • EPoint 𝐷

Q5:

An object is thrown up in the air, and it falls back down to the ground. The height, , of the object above the ground over time, 𝑡 , is shown on the graph by the blue line. What is the speed of the ball at 𝑡 = 4 s?

Q6:

A ball is thrown up in the air, and it falls back down to the ground. The height, , of the ball above the ground over time, 𝑡 , is shown on the graph by the blue line. Which of the five dashed lines shown on the graph is a tangent to the blue line at 𝑡 = 3 s ?

  • AThe black line
  • BThe purple line
  • CThe green line
  • DThe red line
  • EThe orange line

Q7:

A ball is thrown up in the air, and it falls back down to the ground. The height, , of the ball above the ground over time, 𝑡 , is shown on the graph by the blue line. What is the speed of the ball at 𝑡 = 2 s?

Q8:

The graph is a displacement-time graph for an object. At which of the labeled points on the graph does the object have the greatest speed?

  • APoint 𝐸
  • BPoint 𝐴
  • CPoint 𝐷
  • DPoint 𝐵
  • EPoint 𝐶

Q9:

A car is driven along a straight road. It starts at rest. It is first driven forward and then slows down and reverses and finally ends up back at its starting point. The displacement of the car along the road over time is shown by the red line on the graph. The blue line is a tangent to the red line at 𝑡 = 1 6 s . Points A and B mark where the blue line crosses grid lines.

What is the speed of the car at 𝑡 = 1 6 s ? Give your answer to 2 significant figures.

  • A 0.95 m/s
  • B 5.0 m/s
  • C 4.0 m/s
  • D 0 m/s
  • E 1.0 m/s

Q10:

An object moves along a straight line. On the graph, the blue line shows the displacement, 𝑑 , of the object from its starting position over time, 𝑡 .

What is his speed 2 seconds after he starts walking?

What is his speed 6 seconds after he starts walking?

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