Question

The position of a body moving along the x-axis at time t is given by $t^2-4t+6$. The distance traveled by body in time interval t= 0 to t = 3 s is

• A. $5m$
• B. $7m$
• C. $4m$
• D. $3m$

Answer 1

Answer: (D)

Answer: (A) 5 m

Explanation:

We're asked to find the distance traveled by the object after the first three seconds of its motion, given its one-dimensional position equation.

Notice that it doesn't ask for the displacement of the particle, it asks for the total distance traveled. With that in mind, we can't simply plug in the t=0 and t=3 s values and have that be the answer, we would have to substitute all values for t:

Since it's asking for the distance traveled, we can disregard the "+6" quantity in the equation, because at time t=0 it obviously hasn't gone anywhere yet. The process is as follows:

$x\left(0\right)=(0{)}^2-4(0)=0$ m

$x\left(1\right)=(1{)}^2-4(1)=-3$ m

$x\left(2\right)=(2{)}^2-4(2)=-4$ m

$x\left(3\right)=(3{)}^2-4(3)=-3$ m

Magnitude of distance travelled from t = 0 s to t = 1 s = |-3 - 0| = 3 m

Magnitude of distance travelled from t = 1 s to t = 2 s = |-4-(-3)| = 1 m

Magnitude of distance travelled from t = 2 s to t = 3 s = |-3-(-4)| = 1 m

Thus the magnitude of distance travelled from t = 0 s to t = 3 s = 3 + 1 + 1 = 5 m.

So option (A) is correct.