Question

A 2.0 kg projectile with initial velocity v = 7.5 m/s experiences the variable force f = -2.0t i^ + 4.0t² j^ N, where t is in s. Calculate the acceleration of the projectile at a given time t. Provide the expressions for both the

x- and y-components of acceleration.

Answer 1

The acceleration of the 2.0 kg projectile at a given time t, with force f = -2.0t i^ + 4.0t² j^ N, is calculated by dividing the force by the mass for each component. The x-component of acceleration is −1.0t m/s², and the y-component is 2.0t² m/s².

Step-by-step explanation:

To calculate the acceleration of the 2.0 kg projectile at a given time t, we need to apply Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration. Given the force f = -2.0t i^ + 4.0t² j^ N, we can find the acceleration by dividing the force by the projectile's mass.

The expressions for the x- and y-components of acceleration at time t are:

• a_x = −2.0t N / 2.0 kg = −1.0t m/s²
• a_y = 4.0t² N / 2.0 kg = 2.0t² m/s²

Therefore, the acceleration vector a(t) at time t is a(t) = −1.0t i^ + 2.0t² j^ m/s².