Question

1. A particle is travelling along a straight path described as = 0.75x . If its position along the x axis is
x= (8t)m, where t is in seconds, determine its speed when t=2s.

Answer 1

Particle A particle is travelling along a straight path described as $y= 0.75x$ .

And, $x=8t \implies y=0.75\times 8t=6t$

So particle path is given by $s=(8t) \ \hat{i} +(6t)\ \hat{j}$

Velocity of Particle $(v)=\frac{ds}{dt}=\frac{d}{dt} (8t) \hat{i} +\frac{d}{dt} (6t) \hat{j}=8\hat{i}+ 6\hat{j}\ m/s$

Or Magnitude will be $|v| =\sqrt{8^2+6^2}=10 \ m/s$