Question : The x and y coordinates of the particle at any time are x=5t-2t² and y=10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t=2s is
a) 5 m/s²
b) -4 m/s²
c) -8 m/s²
d) 0
Doubt by Trishna
Solution :
x=5t-2t²
y=10t
r=xi+yj
r=(5t-2t²)i+(10t)j
r=(5t-2t²)i+(10t)j
v=dr/dt
v = d[(5t-2t²)i+(10t)j]/dt
v = d[(5t-2t²)i+(10t)j]/dt
v = (5-4t)i+10j
a = dv/dt
a = d[(5-4t)i+10j]/dt
a = (0-4)i+0j
a = -4i
a = -4i
acceleration is independent of time t. It remains constant at all time
The acceleration at t=2sec is -4 m/s²
Hence, b) -4 m/s² would be the correct option.