Question

if the velocity of a car moving with uniform velocity changes from 25 m/s to 50 m/s in 10 second . a) what is the acceleration of the car .b) what is the displacement by the car during the time interval​

Answer 1

Given :

• Final velocity, v = 50 m/s
• Initial velocity, u = 25 m/s
• Time, t = 10 seconds

To find :

• Acceleration, a &
• Displacement, s

According to the question,

➞ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

➞ Substituting the values,

➞ 50 = 25 + a × 10

➞ 50 - 25 = 10a

➞ 25 = 10a

➞ 25 ÷ 10 = a

➞ 2.5 = a

• So,the acceleration is 2.5 m/s².

➞ s = ut + ½ at²

Where,

• a = Acceleration
• u = Initial velocity
• v = Final velocity
• s = Distance/ Displacement

➞ s = 25 × 10 + ½ × 2.5 × 10 × 10

➞ s = 250 + 2.5 × 5 × 10

➞ s = 250 + 125

➞ s = 375

• So,the displacement of the car during the time interval is 375 meters.

Answer 2

Given:

• Velocity of a car moving with uniform velocity changes from 25 m/s to 50 m/s in 10 second.

To Find:

• What is the acceleration of the car & displacement by the car during the time interval.

Solution:

Here we have:

• $\sf{Final \: Velocity \: (v) = 50 \: m/s}$

• $\sf{Initial \: Velocity \: (v) = 25 \: m/s}$

• $\sf{Time \: (t) = 10 \: sec}$

$\sf\underline{\bigstar{According \: to \: question \: now :}}$

We know the first equation of motion:

$\boxed{\tt\green\star \: {v = u + at}}}$

Substituting values in our Equation:

$\\ :\implies\rm{50 = 25 + a \times 10} \\ \\ :\implies\rm{50 - 25 = 10a} \\ \\ :\implies\rm{25 = 10a} \\ \\ :\implies\rm{a = \dfrac{\cancel{25}}{\cancel{10}}} \\ \\ :\implies{\boxed{\sf{\red{a = 2.5}}}} \: \bigstar$

We know the second equation of motion:

$\boxed{\tt\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>\star \: {s = ut + \frac{1}{2} {at}^{2}</strong><strong>}$

Substituting values in our Equation:

$\\ :\implies\rm{s = 25 \times 10 + \frac{1}{2} \times 2.5 \times 10 \times 10} \\ \\ :\implies\rm{s = 250 + 2.5 \times 5 \times 10} \\ \\ :\implies\rm{s = 250 + 125} \\ \\ :\implies{\boxed{\sf{\blue{s = 375}}}} \: \bigstar$

Thus,

$\therefore$ The acceleration of the car is 2.5 m/s² and the displacement of the car is 375 meters.