We all know that the Space Shuttle Solid Rocket Boosters (SRB) were the pair of large solid rockets used by the United States' NASA Space Shuttle during the first two minutes of its powered flight. Together, they provided about 83% of liftoff thrust for the Space Shuttle.
When they are jettisoned, it seems they are still giving off some thrust. In the first seconds after this, would it have been possible for these to turn into the direction of the Space Shuttle and collide with it?
No, they don't have sufficient thrust when they're jettisoned to catch up with Space Shuttle accelerating away:
The SRBs are jettisoned from the space shuttle at high altitude, about 146,000 ft (45 km). SRB separation is initiated when the three solid rocket motor chamber pressure transducers are processed in the redundancy management middle value select and the head-end chamber pressure of both SRBs is less than or equal to 50 psi (340 kPa). A backup cue is the time elapsed from booster ignition.
The separation sequence is initiated, commanding the thrust vector control actuators to the null position and putting the main propulsion system into a second-stage configuration (0.8 second from sequence initialization), which ensures the thrust of each SRB is less than 100,000 lbf (440 kN). Orbiter yaw attitude is held for four seconds, and SRB thrust drops to less than 60,000 lbf (270 kN).
At the same time, Space Shuttle continues thrusting with its three SSME, each at roughly 418,000 lbf (1,860 kN) for 5,250 kN (1,180,000 lbf) total thrust to the remaining mass of the launch vehicle.
So if we assume worst case, SRB dry mass is 82,879 kg, and at maximum separation thrust can achieve acceleration of 3.26 m/s² which will rapidly decrease as residual solid propellants burn to exhaustion, while the remaining Space Shuttle Orbiter + External Tank configuration weighs approximately 874,290 kg when full (it wouldn't be even close to that on SRB separation) for a minimum acceleration of 6 m/s². So even assuming absolute worst case, thrust of Space Shuttle SRBs on jettison isn't enough for them to catch up with the Space Shuttle.
I used numbers from Braeunig.
The SRBs have smaller solid separation motors, 8 on each, which simultaneously fire to push the boosters safely away from the orbiter/ET.
Here's a video showing them in action -- they're powerful enough to give the external tank a good scorching. You can see the separation is designed to turn the boosters slightly outward so any remaining SRB thrust takes them further away from the stack, and what little air there is at 45km altitude also helps to drive them aside.
Conceivably, if the forward separation motors failed while the aft ones fired, the booster could be driven inward instead of outward. This is a very unlikely scenario.
