Question

A car starts from an initial velocity of 10m/s and accelerates at 2.5m/s².how long will it take the car to reach a speed of 40m/s.. How far doea the car travel during this time?

Answer 1

The car will take 12 seconds to reach a speed of 40 m/s. During this time, it will travel a distance of 300 meters.

Step-by-step explanation:

To find the time it takes for the car to reach a speed of 40 m/s, we can use the equation:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Plugging in the values, we have:

40 = 10 + 2.5t

Simplifying the equation:

2.5t = 40 - 10

2.5t = 30

t = 30 / 2.5

t = 12 seconds

To find the distance traveled by the car during this time, we can use the equation:

s = ut + (1/2)at²

Where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.

Plugging in the values:

s = 10 × 12 + (1/2) × 2.5 × (12)²

s = 120 + (1/2) × 2.5 × 144

s = 120 + 180

s = 300 meters

Answer 2

Step-by-step explanation:

Given,

Initial velocity of the car (u) = 10m/s

Acceleration of the car (a) = 2.5m/s²

Final velocity of the car (v) = 40m/s

(i) Let,

Time taken by the car to reach the final velocity = t

So,

By the problem,

=> v = u + at (According to first equation of motion)

• [On putting the values]

=> 40 = 10 + 2.5t

• [On subtracting both sides with 10]

=> 40 - 10 = 10 + 2.5t - 10

• [On Simplification]

=> 30 = 2.5t

• [On dividing both sides with 2.5]

`= > (30)/(2.5) = (2.5t)/(2.5)`

• [On Simplification]

=> t = 12

Hence,

Required time taken by the car to reach a speed of 40m/s is 12 seconds. (Ans)

(ii) Let,

Distance traveled by the car within this time be = s

So,

By the problem,

=> s = ut + 1/2at² (According to second equation of motion)

• [On putting the values]

`= > s = 10 * 12 + (1)/(2) * 2.5 * {12 }^(2)`

• [On Simplification]

`= > s = 10 * 12 + (1)/(2) * 2.5 * 144`

• [On multiplying]

=> s = 120 + 180

• [On adding]

=> s = 300

Hence,

Required distance covered by the car within that time is 300m (Ans)