Question

A roller coaster's velocity at the top of the hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the coaster?

Answer 1

Answer:

Given :

• A roller coaster velocity at the top of the hill is 10 m/s.
• Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s.

To Find :-

• What is the acceleration of the coaster.

Formula :-

$\bigstar$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

Solution :-

Given :

• Initial Velocity (u) = 10 m/s
• Final Velocity (v) = 26 m/s
• Time Taken (t) = 2 seconds

According to the question by using the formula we get,

$\implies \sf 26 =\: 10 + a(2)$

$\implies \sf 26 =\: 10 + 2a$

$\implies \sf 26 - 10 =\: 2a$

$\implies \sf 16 =\: 2a$

$\implies \sf \dfrac{\cancel{16}}{\cancel{2}} =\: a$

$\implies \sf 8 =\: a$

$\implies \sf\bold{\red{a =\: 8\: m/s^2}}$

$\therefore$ The acceleration of the coaster is 8 m/s².

EXTRA INFORMATION :

✭ First Equation Of Motion :

$\leadsto \sf\bold{\purple{v =\: u + at}}$

✭ Second Equation Of Motion Formula :

$\leadsto \sf\bold{\purple{s =\: ut + \dfrac{1}{2}at^2}}$

✭ Third Equation Of Motion Formula :

$\leadsto \sf\bold{\purple{v^2 =\: u^2 + 2as}}$

where,

• s = Distance Covered or Distance Travelled
• u = Initial Velocity
• v = Final Velocity
• a = Acceleration
• t = Time Taken