Question

A particle starts with an initial velocity 2.5 M per second along the positive x-axis and it accelerates uniformly at the rate 0.5 m per second square find the distance travelled by it in first 2 seconds and how much time does it take to reach there velocity 7.5 M per second also find how much distance will it cover before reaching the velocity 7.5 M per second

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{(i)Distance=6\:m}}}$

$\green{\therefore{\text{(ii)Time=10\:sec}}}$

$\green{\therefore{\text{(iii)Distance=50\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a particle moving with initial speed and uniform acceleration.

• At first we have to find the distance travelled in first 2 sec.

• Second, we have to find the time taken to reach velocity 7.5 m/s.

• At last, we have to find the distance travelled in reaching the velocity of 7.5 m/s.

$\green{\underline \bold{Given :}} \\ \\ \implies \text{Initial \: Velocity(u) = 2.5 \: m/s }\\ \\ \implies \text{Acceleration(a) = 0.50 \: m/ }{s}^{2} \\ \\ \implies \text{Time(t) = 2 \: sec} \\ \\ \red{\underline \bold{To \: find : }} \\ \\ \implies \text{Distance \: travelled \: in \: 2 \: sec =?} \\ \\ \implies \text{ Time \: taken \: to \: reach \: velocity \: 7.5 \: m/s =? }\\ \\ \implies \text{Distance \: travelled \: in \: reaching \: velocity \: 7.5 \: m/s = ?}$

• According to given question :

$\bold{For\:first\:question:}\\\\ \bold{By \: Third \: equation \: of \: motion : } \\ \\ :\implies s = ut + \frac{1}{2}a {t}^{2} \\ \\ :\implies s = 2.5 \times 2 + \frac{1}{2} \times 0.50 \times {2}^{2} \\ \\ :\implies s = 5 + 0.25 \times 4 \\ \\ :\implies s = 5 + 1 \\ \\ \green{:\implies s = 6 \: m}$

$\bold{For \: second \: question : } \\ \\ \bold{By \: First \: equation \: of \: motion : } \\ \\ :\implies v = u + at \\ \\ \implies 7.5 = 2.5 + 0.5 \times t \\ \\ :\implies 7.5 - 2.5 = 0.5t \\ \\ \implies t = \frac{5}{0.5} \\ \\ \green{ :\implies t = 10 \: sec}$$\bold{For \: third \: question : } \\ \\ \bold{By \: Second \: equation \: of \: motion : } \\ \\ :\implies {v}^{2} = {u}^{2} + 2as \\ \\ :\implies ({7.5})^{2} = ({2.5})^{2} + 2 \times 0.5 \times s \\ \\ :\implies 56.25 = 6.25 + s \\ \\ :\implies s = 56.25 - 6.25 \\ \\ \green{:\implies s = 50 \: m}$