Question

A car going 45 m/s accelerates to pass a truck. Five seconds later the car is going 75 m/s. Calculate the acceleration of the car using the units of meters per second.

Answer 1

» Given Question:

A car going 45 m/s accelerates to pass a truck. Five seconds later the car is going 75 m/s. Calculate the acceleration of the car using the units of meters per second.

» Required Solution:

${\underline {\underline {\rm {\green { Given: }}}}}$

• u ( intial velocity ) = 45 m/s

• v ( final velocity ) = 75 m/s

• t ( time taken ) = 5 s

${\underline {\underline {\rm {\green { To \: find: }}}}}$

• a ( acceleration ) = ?

${\underline {\underline {\rm {\green { Calculation: }}}}}$

In order to find acceleration, we will use here first equation of motion,

• Formula -$\red \bigstar$ ${\boxed {\tt { v = u + at }}}$

Substituting values, we get -

$\tt { :\implies 75 = 45 + 5a }$

$\tt { :\implies 5a = 75 - 45 }$

$\tt { :\implies 5a = 30 }$

$\tt { :\implies 5a = 30 }$

$\tt { :\implies a = \dfrac{30}{5} }$

$\tt\red { :\implies a = 6 }$

Therefore, acceleration of the car is $\tt { 6 \: {m/ s}^{ 2} }$.

Also we can find it using acceleration formula, ad acceleration is the change in the velocity with time therefore,

• Formula - -$\red \bigstar$ ${\boxed {\tt { a = \dfrac{v-u}{t} }}}$

Substituting values, we get -

$\tt { :\implies a = \dfrac{75-45}{5} }$

$\tt { :\implies a = \dfrac{30}{5} }$

$\tt\red { :\implies a = 6 }$

Therefore, acceleration of the car is $\tt { 6 \: {m/ s}^{ 2} }$.

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Additional Information:

• Acceleration of the body is defined as the rate of change of its velocity with time.

• SI unit of acceleration is $\tt { {m/ s}^{ 2} }$.

• Acceleration is a vector quantity.

THREE EQUATIONS OF MOTION:

First equation of motion:

• $\red \bigstar$ ${\boxed {\tt { v = u + at }}}$

Second equation of motion:

• $\red \bigstar$ ${\boxed {\tt { s = ut + \dfrac{1}{2}a{t}^{2} }}}$

Third equation of motion:

• $\red \bigstar$ ${\boxed {\tt {2as={v}^{2} - {u}^{2} }}}$

Where,

• v denotes final velocity
• u denotes intial velocity
• a denotes acceleration
• t denotes time
• s denotes distance/displacement

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Answer 2

Explanation:

$\red{formula = a = \frac{v - u}{t}}$

$a = \frac{75 - 45}{5}$

$a = \frac{30}{5}$

$a = 6$

acceleration = 6