Lesson Worksheet: Impulse and Momentum Mathematics

In this worksheet, we will practice relating the impulse on a body to the change of momentum of the body.


A constant force acted on a body of mass 6 kg. As a result, its speed changed from 37 km/h to 49 km/h. Calculate the magnitude of the impulse of this force on this body.


A smooth sphere of mass 1,412 g was moving horizontally in a straight line at 13.5 m/s when it hit a smooth vertical wall and rebounded at 9 m/s. Determine the magnitude of the impulse exerted on the sphere.


The given figure shows a force-time graph for a force acting in a constant direction on a body moving along a smooth horizontal plane. Using the information provided, calculate the magnitude of the force’s impulse.


A constant force acted on a body of mass π‘š changing its speed from 9 m/s to 54 km/h. Given that the impulse of the force was 5.82 Nβ‹…s, determine the value of π‘š.


The forces Fij=π‘Ž+3, Fij=βˆ’3+𝑏, and Fij=π‘Žβˆ’3 acted on a body for 3 seconds. If their combined impulse on the body was Iij=3βˆ’6, find the values of π‘Ž and 𝑏.

  • Aπ‘Ž=2, 𝑏=βˆ’8
  • Bπ‘Ž=4, 𝑏=βˆ’2
  • Cπ‘Ž=4, 𝑏=βˆ’8
  • Dπ‘Ž=2, 𝑏=βˆ’2


Three forces, Fijk=(βˆ’5βˆ’2+2)N, Fjk=(βˆ’3)N, and Fijk=(βˆ’βˆ’5βˆ’2)N, where i, j, and k are three mutually perpendicular unit vectors, acted on a body for 3 seconds. Find the magnitude of their combined impulse on the body.

  • A27 Nβ‹…s
  • B3√73 Nβ‹…s
  • C3√89 Nβ‹…s
  • D9 Nβ‹…s


A body of mass 5 kg fell vertically from rest. It reached the water’s surface after 2.2 seconds. Then, as it moved through the water, it descended vertically at a constant speed such that it covered 3.9 m in 1.5 seconds. Find the magnitude of the change in its momentum as a result of its impact with the water.


The given figure shows a force-time graph. At time 𝑑 seconds, where 𝑑⩾0, the force is given by 𝐹=(π‘‘βˆ’2)N. Find the impulse over the first four seconds.

  • A4 Nβ‹…s
  • B8 Nβ‹…s
  • C163 Nβ‹…s
  • D83 Nβ‹…s


A ball of mass 400 g moves perpendicularly toward a vertical wall at a constant speed of 16 m/s. Given that the wall exerts an impulse of 11 Nβ‹…s on the ball during the impact, find the rebound speed of the ball.

  • A5.75 m/s
  • B27.5 m/s
  • C11.5 m/s
  • D19.5 m/s


A sphere of mass 83 g fell vertically from a height of 8.1 m onto a section of horizontal ground. It rebounded and reached a height of 3.6 m. Given that the duration of the impact was 0.42 seconds, and the acceleration due to gravity is 9.8 m/s2, find the average impact force to the nearest two decimal places.

This lesson includes 31 additional questions and 270 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.