Question

A person is moving in a circle of radius r with constant speed v. The change in velocity in moving from A to B is (∠ AOB = 40°) ____________.

Options

• 2v cos (40°)

• 2v sin (40°)

• 2v cos (20°)

• 2v sin (20°)

Answer 1

A person is moving in a circle of radius r with constant speed v. The change in velocity in moving from A to B is (∠ AOB = 40°) 2v sin (20°).

Explanation:

`"Here"  absvec("v"_2) = absvec("v"_1) = "v"`

`abs(Deltavec "v") = abs (vec"v"_2 - vec "v"_1)`

`= sqrt ("v"_2^2 + "v"_1^2 - 2"v"_1"v"_2 "cos"  theta)`

`= sqrt ("v"^2 + "v"^2 - 2"v"^2 "cos"  theta)`

`= sqrt (2"v"^2 (1 - "cos"  theta)) = sqrt (2"v"^2 2"sin"^2 (theta//2))`

`= 2"v"  "sin" (theta//2)`

`"As"  theta = 40°,`

`therefore abs(Deltavec "v") = 2"v"  "sin" (20°)`