Question

a car starts from rest and travels with a uniform acceleration. the car travels 100 m in 5s . what will be its final velocity ​

Answer 1

40 m/s is the required answer.

GIVEN:

• Initial velocity, u
• Distance travelled by the car, s = 100 m
• Time, t = 5 sec

TO FIND:

Final velocity, v

FORMULAE:

• According to first equation of motion, v = u + at.

• According to second equation of motion, s = ut + ( at²) / 2

Where a is the acceleration.

SOLUTION:

STEP 1: To find acceleration

$s = ut + \frac{1}{2} a {t}^{2} \\ \\ 100 = (0 \times 5) + ( \frac{1}{2} \times a \times {(5)}^{2} ) \\ \\ 100 = 0 + ( \frac{1}{2} \times a \times \times 25 ) \\ \\ 100 = \frac{25 \times a}{2} \\ \\ a = \frac{100}{25} \times 2 \\ \\ a = 4 \times 2 \\ \\ a = 8 \: \dfrac{m}{ {s}^{2} }$

Acceleration is 8 m/s²

STEP 2: To find final velocity

$v = u + at \\ \\ v = 0 + (8 \times 5) \\ \\ v = 8 \times 5 \\ \\ v = 40 \: \frac{m}{s}$

ANSWER:

The final velocity of the car is 40 m/s.

OTHER FORMULAE:

• First equation of motion, v = u + at

• Second equation of motion, s = ut + ( at²) / 2

• Third equation of motion, v² - u² = 2as

• These three equations of motion are valid only if acceleration is constant.

• Constant acceleration is the one that does not change with time.