Question:
An object, moving with velocity 5 m/s, undergoes an acceleration of 1 m/s$^2$ at time $t = 0$. If the object has a mass of 1 kg, the kinetic energy (KE) of the object at time $t = 5$ s is
An object, moving with velocity 5 m/s, undergoes an acceleration of 1 m/s$^2$ at time $t = 0$. If the object has a mass of 1 kg, the kinetic energy (KE) of the object at time $t = 5$ s is
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Always calculate the final velocity at the specific timestamp first before attempting to find the energy.
Updated On: May 1, 2026
- KE = 12.5 Joules
- KE = 20 Joules
- KE = 30 Joules
- KE = 50 Joules
- KE = 0 Joules
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The Correct Option is D
Solution and Explanation
Concept:
The Kinetic Energy ($KE$) of an object is determined by its mass and its instantaneous velocity at a specific moment, given by the formula: \[ KE = \frac{1}{2}mv^2 \]
Step 1: Determine the velocity at $t = 5$ seconds.
Using the first equation of motion for constant acceleration: \[ v = u + at \] Given:
• Initial velocity ($u$) = 5 m/s
• Acceleration ($a$) = 1 m/s$^2$
• Time ($t$) = 5 s \[ v = 5 + (1 \times 5) = 5 + 5 = 10 \text{ m/s} \]
Step 2: Calculate the Kinetic Energy.
Substitute the final velocity and the given mass ($m = 1$ kg) into the $KE$ formula: \[ KE = \frac{1}{2} \times 1 \text{ kg} \times (10 \text{ m/s})^2 \] \[ KE = \frac{1}{2} \times 1 \times 100 \] \[ KE = 50 \text{ Joules} \]
The Kinetic Energy ($KE$) of an object is determined by its mass and its instantaneous velocity at a specific moment, given by the formula: \[ KE = \frac{1}{2}mv^2 \]
Step 1: Determine the velocity at $t = 5$ seconds.
Using the first equation of motion for constant acceleration: \[ v = u + at \] Given:
• Initial velocity ($u$) = 5 m/s
• Acceleration ($a$) = 1 m/s$^2$
• Time ($t$) = 5 s \[ v = 5 + (1 \times 5) = 5 + 5 = 10 \text{ m/s} \]
Step 2: Calculate the Kinetic Energy.
Substitute the final velocity and the given mass ($m = 1$ kg) into the $KE$ formula: \[ KE = \frac{1}{2} \times 1 \text{ kg} \times (10 \text{ m/s})^2 \] \[ KE = \frac{1}{2} \times 1 \times 100 \] \[ KE = 50 \text{ Joules} \]
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