Question

A constant net force of 200 N is excerted to accelerate a cart from rest to a velocity of 40 m/s in 10 s. What is the mass of the cart?

Answer 1

the required answer is 50 kg

GIVEN:

• force, f= 200 N

• initial velocity, u =0 m/ s

• final velocity , v= 40 m/ s

• time, t= 10 s

TO FIND:

mass of the cart , m

KEYS:

• f.... force
• a.... Acceleration
• u.... initial velocity
• v..... final velocity
• t...... time
• m.... mass
• s..... displacement

FORMULAE:

• according to Newton's second law of motion,

$f = ma$

• according to first equation of motion,

$v = u + at$

SOLUTION:

STEP 1: TO FIND ACCELERATION USING FIRST EQUATION OF MOTION.

$v = u + at \\ \\ 40 = 0 +a (10) \\ \\ 40 = 10a \\ \\ a = \frac{40}{10} \\ \\a = 4 \: \frac{m}{ {s}^{2} }$

acceleration, a = 4m/s^2

STEP 2: TO FIND MASS

$f = ma \\ \\ m = \frac{f}{a} \\ \\ m = \frac{200}{4} \\ \\ m = 50 \: kg$

ANSWER:

the mass of the cart is 50 kg.

OTHER FORMULAE:

• FIRST EQUATION OF MOTION

v= u+at

• SECOND EQUATION OF MOTION

s=ut+(1/2)at^2

• THIRD EQUATION OF MOTION

v^2-u^2=2as