Question

How long does it take to accelerate a car from a speed of 90 km/h to a speed of 108 km/h at an acceleration of 1 m/s^2

Answer 1

Answer:

Given:

Initial velocity = 90 km/hr

Final velocity = 108 km/hr

Acceleration = 1 m/s²

To find:

Time taken to achieve the final Velocity

Calculation:

First we need to convert the unit of speed from Km/hr to m/s

90 km/hr = 90 × (5/18) = 25 m/s and

108 km/hr = 108 × (5/18) = 30 m/s

$v = u + at$

$= > t = \dfrac{v - u}{a}$

$= > t = \dfrac{30 - 25}{1}$

$= > t = \dfrac{5}{1}$

$= > t = 5 \: sec$

So final answer :

$\boxed{ \red{ \bold{ \huge{time = 5 \: sec}}}}$

Additional information:

• Both velocity and acceleration are vector Quantities having both magnitude and direction.
• The equations of Kinematics can be applied only when the Acceleration is considered constant.
• For conversion of Km/hr to m/s , use the trick of multiplying with (5/18) with km/hr data.

Answer 2

Solution :

⏭ Given:

✏ Initial velocity of car = 90kmph

✏ Final velocity of car = 108kmph

✏ Acceleration = 1$\sf{\dfrac{m}{s^2}}$

⏭ To Find:

✏ Time interval...

⏭ Concept:

✏ Acceleration is defined as ratio of change in velocity to the time interval.

⏭ Formula:

✏ As per first equation of kinematics, Formula of acceleration in terms of change in velocity and time interval is given by

$\bigstar \: \underline{ \boxed{ \bold{ \sf{ \pink{ \large{a = \frac{v - u}{t}}}}}}} \: \bigstar$

⏭ Terms indication:

✏ a denotes acceleration

✏ v denotes final velocity

✏ u denotes initial velocity

✏ t denotes time interval

⏭ Conversation:

✏ 1km = 1000m

✏ 1h = 3600s

✏ 1kmph = 5/18mps

• 90kmph = 25mps
• 108kmph = 30mps

⏭ Calculation:

$\implies \sf \: a = \dfrac{v - u}{t} \\ \\ \implies \sf \: 1 = \dfrac{30 - 25}{t} \\ \\ \implies \sf \: t = 30 - 25 \\ \\ \implies \: \underline{ \boxed{ \bold{ \sf{ \orange{ \large{t = 5 \: sec}}}}}} \: \gray{ \bigstar}$

⏭ Additional information:

• Velocity and acceleration both are vector quantities.
• Acceleration can be positive, negative and zero.
• Vector quantity has both magnitude and direction.