Question

A car is stopped at a red light. When the light turns green, the driver accelerates the car at a constant rate of +5.0 m/s2 for 7.0 seconds. The car’s total displacement is? what is the car's final velocity?

Answer 1

Given :

• Initial velocity (u) = 0 m/s
• Acceleration (a) = 5 m/s²
• Time interval (t) = 7 s

To FinD :

• Displacement of the car

SolutioN :

Used 1st equation of Kinematics :

$\longrightarrow {\boxed{\sf{v\ =\ u\ +\ at}}} \\ \\ \longrightarrow \sf{v\ =\ 0\ +\ 5\ \times\ 7} \\ \\ \longrightarrow \sf{v\ =\ 0\ +\ 35} \\ \\ \longrightarrow \sf{v\ =\ 35} \\ \\ \underline{\sf{\therefore \: Final\ velocity\ of\ car\ is\ 35\ ms^{-1}}}$

$\rule{150}{1}$

Now, use formula of velocity for calculating Displacement :

$\longrightarrow \boxed{\sf{Velocity\ =\ \dfrac{Displacement}{time}}} \\ \\ \longrightarrow \sf{Displacement\ =\ Velocity\ \times\ time} \\ \\ \longrightarrow \sf{Displacememt\ =\ 35\ \times\ 7} \\ \\ \longrightarrow \sf{Displacement\ =\ 245} \\ \\ \underline{\sf{\therefore \: Displacement\ of\ car\ is\ 245\ m}}$

Answer 2

⋆ Given ⋆

A car is stopped at a red light. When the light turns green, the driver accelerates the car at a constant rate of +5.0 m/s² for 7.0 seconds.

◘ Initial velocity, u= 0

◘ Acceleration, a = 5 m/s²

◘ Time interval, t = 7 secs

⋆ To Find ⋆

◘ The car’s total displacement (s).

◘ The car's final velocity (v).

⋆ Solution ⋆

We know,

s = ut + 1/2 at²

Substituting the values :-

⇒ s = 0(7) + 1/2 × 5(7)²

⇒ s = 1/2 × 5 × 49

⇒ s = 1/2 × 245

⇒ s = 122.5 m

Hence, the car’s total displacement is 122.5 m.

____________________

We also know that,

v = u + at

Substituting the values :-

⇒ v = 0 + 5(7)

⇒ v = 35 m/s

Hence, the car’s final velocity is 35 m.

Note that, the acceleration is positive and constant, this means, the car hasn't decreased its velocity. So, here the displacement becomes equal to the distance.