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, ⃑𝐹=ο€»βˆ’5βƒ‘π‘–βˆ’2⃑𝑗+2βƒ‘π‘˜ο‡οŠ§N, ⃑𝐹=ο€»βƒ‘π‘—βˆ’3βƒ‘π‘˜ο‡οŠ¨N, and ⃑𝐹=ο€»βˆ’βƒ‘π‘–βˆ’5βƒ‘π‘—βˆ’2βƒ‘π‘˜ο‡οŠ©N, where ⃑𝑖, ⃑𝑗, and βƒ‘π‘˜ are three mutually perpendicular unit vectors, acted on a body for 3 s. 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 s. Then, as it moved through the water, it descended vertically with a constant speed such that it covered 3.9 m in 1.5 s. 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 s, 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 s, and the acceleration due to gravity is 9.8 m/s2, find the average impact force to the nearest two decimal places.

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