Question

A rocket-powered hockey puck moves on a horizontal frictionless table. The figures shows graphs of vx and vy, the x- and y-components of the puck's velocity. The puck starts at the origin.

Part A

What is the magnitude of the puck's acceleration at t = 5 s?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Concepts and reason

The required concepts to solve the given question are the velocity of the object and Kinematics equations.

First consider the given graphs that show the relation between the velocities versus time of the hockey pucks. Now by using the kinematics relation, obtain the expression for acceleration of the pucks. Finally, apply the given values to the equation and calculate the magnitude of acceleration.

Fundamentals

Velocity is the rate of change of displacement. Acceleration is the rate of change of velocity. All these are vector quantities.

Acceleration of the object can be expressed as,

Here, is the acceleration, is the velocity and is the time.

The equation of magnitude of acceleration is,

Here, is the -component of the acceleration, and is the -component of the acceleration.

Express the acceleration of the hockey puck in terms of velocity and time.

Acceleration of the puck is the derivative of velocity.

Substitute for , and for in the equation to calculate the .

Substitute for , and for in the equation to calculate the .

The equation of magnitude of acceleration is,

Here, is the -component of the acceleration, and is the -component of the acceleration.

Substitute for and for .

Ans:

Magnitude of the acceleration at is .