Question

A car traveling 60 km/h accelerates at the rate of 2.0 m/s2. How much time is required for the car to reach a speed of 90 km/h?

Answer 1

Answer:

4.165 sec

Explanation:

According to the given question,

u = initial velocity = 60 km/h = 60×1000/3600 = 16.67 m/s

v = final velocity = 90 km/h = 90×1000/3600 = 25

a = acceleration = 2 m/s^2

t = time

And we are asked to find the time required for the car to reach the final velocity as 90 km/h.

We know,

• v = u+at

Putting the values we get,

• 25 = 16.67 + 2t

• 2t = 25-16.67

• 2t = 8.33

• t = 8.33/2

• t = 4.165 sec

Thus the car will take 4.165 sec to attain the final velocity of 90 km/h if it's acceleration is 2 m/s^2 and initial velocity is of 60 km/h.

Answer 2

$\large{\underline{\boxed{{t = 4.16 s}}}$

Given:-

Initial velocity (u) = 60 km/hr

change, it in to its SI unit.

60 × 5/18 = 16.67m/s

Acceleration = 2.0 m/s²

Final velocity (v) = 90 km/hr

90 × 5/18 = 25 m/s

To find :-

Time required to reach v = 48 m/s.

Solution:-

We know that when the acceleration of a body is constant we use equation of motion.

Form 1st equation of motion.

$\large{\underline{\boxed{ </strong><strong>v</strong><strong> </strong><strong>=</strong><strong>u</strong><strong> </strong><strong>+</strong><strong> </strong><strong>at</strong><strong>}}}$

Let it takes "t" time.

put the given value in equation we get,

$\implies$ 25 = 16.67 + 2 × t

$\implies$ 25 - 16.67= 2t

$\implies$ 8.33 = 2t

$\implies$ t = 4.165 ~ 4.16 s.

hence, the time taken to reach the final velocity is 4.16 second.

Others equation of motion that is used to solve kinematics problems are :-

$\boxed{\sf</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>s = ut + \frac{1}{2} a {t}^{2} </strong><strong> </strong><strong>}}$

$\boxed{\sf</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{ </strong><strong>{v}^{2} = 2as + {u}^{2} </strong><strong>}}$

Note :- These equation of motion is valid when acceleration is constant.