Question

A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400m in 20s. Find its acceleration. Find the force acting on it if it's mass is 7 tonnes

Answer 1

ɢɪᴠᴇɴ :-

• Initial velocity (u) = 0m/s --(At rest)
• Distance travelled (s) = 400m
• Time taken (t) = 20s

ᴛᴏ ғɪɴᴅ :-

• Acceleration (a)
• Force (F)

sᴏʟᴜᴛɪᴏɴ :-

On using 1st equation of motion, we get,

➦ v = u + at

➭ v = 0 + a×20

➭ v = 20a. --(1)

On using 3rd equation of motion, we get,

➦ v² - u² = 2as

➭ v² - (0)² = 2a × 400

➭ v² = 800a

➭ (20a) ² = 800a. --(from-1)

➭ 400a² = 800a

➭ a² = 800a/400

➭ a² = 2a

➭ a = 2a/a

➭ a = 2 m/s²

Hence,

• Acceleration (a) = 2 m/s²

Now,

We know that,

➦ 1 ton = 1000 kg

So,

➦ 7 tonnes = 7 × 1000 = 7000 kg

Now,

• Mass(m) = 7000 kg
• Acceleration (a) = 2 m/s²

We know that,

➦ Force = Mass × Acceleration

➦ F = m × a

➦ F = 7000 × 2

➦ F = 14000N

Hence,

• Force (F) = 14000 N

Answer 2

Given:-

• Initial velocity =0m/s

• Distance covered =400m

• Time taken =20s

• Mass =7 tonnes.

To Find:-

• Acceleration of truck.

• Force acting on it.

Solution :-

By using 2nd equation of motion

☛ s=ut +1/2at²

☛ 400 =0×20 + 1/2× a × 20²

☛ 400=1/2× 400 ×a

☛400=200×a

☛ a=400/200

☛ a =2m/s²

∴ The acceleration of truck is 2m/s².

Now,

we have calculate force acting on it

we know that, Force is the product of mass and acceleration.

Mass =7 tonnes

1 ton =1000kg

∴ 7 tonnes =7×1000=7000kg

☛ F =m×a

☛ F = 7000× 2

☛ F = 14000 N.

∴ The Force acting on it is 14000 N.