An object moves on level ground such that it first travels due east and then due north

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

An object moves on level ground such that it first travels

a\,\text{m}

due east and then

b\,\text{m}

due north, where

a

and

b

are positive constants. (i) Write an algebraic expression for the total distance travelled in terms of

a

and

b

. (ii) Derive an expression for the magnitude of the object’s displacement in terms of

a

and

b

. (iii) If

b = 3a

, obtain the simplified ratio of the distance travelled to the magnitude of displacement. (iv) Taking

a = 50\,\text{m}

, calculate the numerical values of (1) the distance travelled, (2) the magnitude of displacement, and (3) the ratio found in part (iii).