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

• A. KE = 12.5 J
• B. KE = 20 J
• C. KE = 30 J
• D. KE = 50 J

Answer 1

The Correct Option is D

Given, $u=5 \,m / s , a=1\, m\,/ s ^{2}$
and mass $=1\, kg$.
So, velocity after $5\,s$ is given as
$v=u+$ at (Equation of motion)
$ v=5+1 \times 5 $
$\Rightarrow v=10\,m / s$
Kinetic energy of object
$KE =\frac{1}{2} m v^{2} $
$=\frac{1}{2} \times 1 \times(10)^{2}=50\, J$

Answer 2

To find the kinetic energy (KE) of the object at time \( t = 5 \, \text{s} \), we first need to determine its velocity at that time.

Given:
- Initial velocity (\( v_0 \)) = \( 5 \, \text{m/s} \)
- Acceleration (\( a \)) = \( 1 \, \text{m/s}^2 \)
- Time (\( t \)) = \( 5 \, \text{s} \)

The velocity at any time \( t \) can be found using the equation of motion:

\[ v = v_0 + at \]

Substituting the given values:

\[ v = 5 \, \text{m/s} + (1 \, \text{m/s}^2 \times 5 \, \text{s}) \]
\[ v = 5 \, \text{m/s} + 5 \, \text{m/s} \]
\[ v = 10 \, \text{m/s} \]

Now, we can calculate the kinetic energy at \( t = 5 \, \text{s} \). The kinetic energy (KE) is given by:

\[ KE = \frac{1}{2} m v^2 \]

where \( m \) is the mass of the object. Substituting the given mass (\( m = 1 \, \text{kg} \)) and the calculated velocity (\( v = 10 \, \text{m/s} \)):

\[ KE = \frac{1}{2} \times 1 \, \text{kg} \times (10 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 1 \times 100 \]
\[ KE = 50 \, \text{J} \]

Therefore, the kinetic energy of the object at time \( t = 5 \, \text{s} \) is \( 50 \, \text{J} \).
Thus Correct Answer is Option 4(D):\(50J\)