A particle is moving along the x-axis with its coordinate with time 't' given by x(t) = 10 + 8t - 3t2. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t) = 5 - 8t3 At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √ upsilon. Then (in m/s) is . Given -

Question

A particle is moving along the x-axis with its coordinate with time 't' given by x(t) = 10 + 8t - 3t2. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t) = 5 - 8t3 At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √ upsilon. Then (in m/s) is . Given - (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

vx=8-6t (Vx)t=1 =2 hati y=5-8t3 Vy=-24t2 (Vy)t=1=-24 hatj Now √v=√(24)2+(2)2=√580 ∴ v=580 m2/s2

vx​=8−6t (Vx​)t=1​=2i^ y=5−8t3 Vy​=−24t2<br/>(Vy​)t=1​=−24j^​ Now v​=(24)2+(2)2​=580​ ∴v=580m2/s2

$v_{x} = 8 - 6 t$
$(V_{x})_{t = 1} = 2 \hat{i}$
$y = 5 - 8 t^{3}$
$V_{y} = - 24 t^{2} < b r / > (V_{y})_{t = 1} = - 24 \hat{j}$
Now
$v = (24)^{2} + (2)^{2} = 580$
$∴ v = 580 m^{2} / s^{2}$