Question

(21) An object moves 6 km due west and then 8 km due north. (1) Find the distance covered by the object. (a) 14 km (b) 12 km (c) 18 km (d) 10 km (ii) Find its displacement. (a) 14 km (b) 12 km (C) 18 km (d) 10 km
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Answer 1

Answer:

m due north. (1) Find the distance covered by the object. (a) 14 km (b) 12 km (c) 18 km (d) 10 km (ii) Find its displacement. (a) 14 km (b) 12 km (C) 18 km (d) 10 km

Answer 2

Answer:

Let’s begin with a particle with an acceleration a(t) is a known function of time. Since the time derivative of the velocity function is acceleration,

  

we can take the indefinite integral of both sides, finding

  

where C1 is a constant of integration. Since

  

, the velocity is given by

  

Similarly, the time derivative of the position function is the velocity function,

  

Thus, we can use the same mathematical manipulations we just used and find

  

where C2 is a second constant of integration.

We can derive the kinematic equations for a constant acceleration using these integrals. With a(t) = a a constant, and doing the integration in (Figure), we find

  

If the initial velocity is v(0) = v0, then

  

Then, C1 = v0 and

  

which is (Equation). Substituting this expression into (Figure) gives

  

Doing the integration, we find

  

If x(0) = x0, we have

  

so, C2 = x0. Substituting back into the equation for x(t), we finally have

  

which is (Equation).