Question

a skier , starting from the rest ,accelerates down a slope at 1.6 m / s sq .how far has he gone in the end of 5.0 s?


please answer with explanation

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \: Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to find out that how far a skier gone in the end of 5.0 seconds that are 5 seconds. Given that, there is a skier, and he start from a rest and accelerate down a slope at 1.6 metre per second sq. that is 1.6 m/s². In short we have to find out the distance. Now let's see how to solve this question properly.

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

$\sf Given \begin{cases} & \sf{Initial \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Acceleration \: = \bf{1.6 \: m/s^{2}}} \\ \\ & \sf{Time \: = \bf{5 \: seconds}} \\ \\ & \sf{Distance \: = \bf{?}} \end{cases}$

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Second equation of motion that is given by

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{s \: = ut + \dfrac{1}{2} \times at^{2}}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

$:\implies \sf s \: = ut + \dfrac{1}{2} \times at^{2} \\ \\ :\implies \sf s \: = 0(5) + \dfrac{1}{2} \times 1.6(5)^{2} \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 1.6(25) \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 40 \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times 40 \\ \\ :\implies \sf s \: = 20 \: m$

Henceforth, he can go 20 m is the distance at which the skier can go far at the end of given time.

${\large \:{\pmb{\sf{\underline{Extra \: shots...}}}}}$

If we are asked to find final velocity then we have to use,

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf 1.6 = \dfrac{v-0}{5} \\ \\ :\implies \sf 1.6 = \dfrac{v}{5} \\ \\ :\implies \sf 1.6 \times 5 = v \\ \\ :\implies \sf 8.0 = v \\ \\ :\implies \sf 8 = v \\ \\ :\implies \sf v = 8 \\ \\ :\implies \sf Final \: velocity \: = 8 \: m/s$

Henceforth, 8 meter per second is the final velocity of the skier

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Acceleration: The term acceleration is a measure of the change in the velocity of an object per unit time.

So, according to the question we have to find out the change in velocity of the object that is acceleration.

${\small{\underline{\boxed{\sf{Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken}}}}}}$

If the velocity of an object is changes from initial value u to the final value v in the time t the acceleration a be

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

The SI unit of acceleration is m/s²