The x and y coordinates of the particle at any time are x=5t-2t2 . . .

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
v=dr/dt 
v = d[(5t-2t²)i+(10t)j]/dt
v = (5-4t)i+10j

a = dv/dt
= d[(5-4t)i+10j]/dt
a = (0-4)i+0j
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.