Question

A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of 400 m in 20s. Find the acceleration and force acting on it; if its mass is 8000kg.​

Answer 1

$\huge{\underline{\underline{\mathrm{\blue{GIVEN:-}}}}}$

• Initial Velocity(u) = 0
• Distance (s) = 400 m
• Time(t) = 20 sec
• Mass(m) = 8000 kg

$\huge{\underline{\underline{\mathrm{\blue{NEED\:TO\:FIND:-}}}}}$

Find the Acceleration and force acting on the truck = ?

$\huge{\underline{\underline{\mathrm{\blue{FORMULA\:USED:-}}}}}$

$\large{\underline{\overline{\bf{\red{s = ut + \frac{1}{2}a{t}^{2}}}}}}$

$\large{\underline{\overline{\bf{\red{Force = mass \times acceleration}}}}}$

$\huge{\underline{\underline{\mathrm{\blue{SOLUTION:-}}}}}$

∴ To find the force, We need to find the acceleration of the truck

Let the Acceleration of the truck be 'a' m/s²

Putting the given values in formula

$\large\bf{s = ut + \frac{1}{2}a{t}^{2}}$

$\longrightarrow$$\rm{ 400 = 0 \times 20 + \frac{1}{2}\times a {20}^{2}}$

$\longrightarrow$$\rm{ 400 = 0 + \frac{1}{2}\times a \times 400}$

$\longrightarrow$$\rm{ 400 = \frac{1}{\cancel{2}} \times \cancel{400}\times a}$

$\longrightarrow$$\rm{ 400 = 200\times a}$

$\longrightarrow$$\rm{ a = \cancel\dfrac{400}{200}}$

$\longrightarrow$$\large{\underline{\overline{\bf{\green{ a = 2 \: m{s}^{-2}}}}}}$

Thus, the Acceleration of the truck = 2 m/s²

∴ Now, we have to find the Force acting upon the truck

Putting the given values in formula

$\large\bf{ Force = Mass \times acceleration}$

$\longrightarrow$$\rm{ Force = 8000 \times 2}$

$\longrightarrow$ $\large{\underline{\overline{\bf{\green{Force = 16000\: N}}}}}$

Hence, the Force acting upon the truck is 16000 N

$\large{\underline{\underline{\mathrm{\blue{FINAL\:ANSWER:-}}}}}$

$\large{\underline{\overline{\bf{\green{Acceleration = 2\: m{s}^{-2}}}}}}$

$\large{\underline{\overline{\bf{\green{Force = 16000 \: N }}}}}$