Question

A race car accelerates from an initial velocity of 10 m/s to a final velocity is 30 m/s in a time interval of 2s. Determine its average acceleration?​

Answer 1

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

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

⠀⠀⠀⠀⠀⠀⠀A race car accelerates from an initial velocity of 10 m/s to a final velocity is 30 m/s in a time interval of 2 seconds.

† According to the statement

• Initial velocity = 10 m/s

• Final velocity = 30 m/s

• Time = 2 seconds

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

Acceleration of a race car which accelerates from an initial velocity of 10 m/s to a final velocity is 30 m/s in a time interval of 2 seconds?

• Acceleration = 10 m/s sq.

${\bigstar \:{\pmb{\sf{\underline{Knowledge \: required...}}}}}$

⋆ 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

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

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{30-10}{2} \\ \\ :\implies \sf a \: = \dfrac{20}{2} \\ \\ :\implies \sf a \: = \cancel{\dfrac{20}{2}} \\ \\ :\implies \sf a \: = 10 \\ \\ :\implies \sf Acceleration \: = 10 \: m/s^{2}$

${\bigstar \:{\pmb{\sf{\underline{Additional \: information...}}}}}$

Distance = It is the length of actual path covered by a moving object in a given time interval.

Displacement = Shortest distance covered by a body in a definite direction is called displacement.

→ Displacement may be positive, negative or zero whereas distance is always positive.

→ Distance is a scaler quantity whereas displacement is a vector quantity both having the same unit.

→ In general magnitude of displacement ≤ Distance.

Speed = Distance travelled by a moving object in unit time interval is called speed i.e., speed Distance/Time. It's scaler quantity and it's SI unit is metre/second

Velocity = Velocity of moving object is defined as the displacement of the object in unit time interval i.e., velocity = Displacement/Time. It's vector quantity and it's SI unit is metre/second.

Acceleration (also defined as) = Acceleration of an object is defined as the rate of change of velocity of the object i.e., Acceleration = Change in velocity/Time. It's vector quantity and SI unit is m/s²