Question

A particle moves rectilinearly with a constant acceleration $1m/s^2$. Its speed after $10$ second is $5m/s$. The distance covered by the particle in this duration is

• A. $25m$
• B. $50m$
• C. $30m$
• D. $20m$

Answer 1

The correct option is C

$30m$

Step 1: Find the initial speed of the particle.
Formula Used: $v=u+at$

Given, aacceleration of the particle
$a=1m/s^2$
Time taken $t=10s$
Final velocity $v=5m/s$
From first equation of motion
$v=u+at$
substituting the values, we get
$5=u+1x10$
$u=-5m/s$
Step 2: Find the distance travelled by the particle.
Now plotting the graph,
Now, Distance travelled by the particle is given as,
Distance travelled
$=\text{Total area under the}v-t\text{graph}$
adding all magnitude
$=2|\frac{1}{2}\times 5\times 5|$
$=25m$
Final Answer: (b)